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When elected, Trump made a big point that his opponent should be investigated and "locked up" over the email controversy. Almost immediately after winning the election, he made tacitly clear he was dropping that as a serious proposal, and to the best of my knowledge he did in fact drop it.

For example I remember him saying something to the effect that it was old news and he wouldn't pursue it, very soon after. I don't recall the DoJ formally being directed/asked to begin an actual investigation or inquiry , although the claim was constantly reused to attack and score points politically and energise his voter base. If the DoJ was at any stage asked to look into it, it's pretty clear by now that they have no interest in taking it further either. Nor do I recall him objecting, or railing against DoJ betrayals, trying to fire anyone in DoJ, or significant action being instigated to force them to investigate/prosecute, for example (as he did with other blocked pledges/issues that mattered to him, such as "Muslim country visitors", Muller inquiry, and the border wall). It really seems as if it's just a rallying cry, of no real interest to him now he has beaten her long ago, but useful to energise and counterattack.

But what about Trump's supporters? They can see these things too. They must have anticipated her arrest and likely trial after such a build-up. They can see she is unarrested. They can see he hasn't made, and never did make, any real effort to get her arrested. They can see he stopped really showing he cared about whether she was arrested long ago (if he ever cared other than as a means to win the election) and that he has no interest whatsoever in having her arrested now or in future. They can see that she is, in effect, already broken as a political contender, and is being left alone in peace, as an individual.

I can think of many things that, if I were a Trump supporter, I might chant. But a broken prominent campaign matter that he's made clear he bailed on directly after winning, and hasn't taken interest in pursuing in the years since? Why does that have any power, in 2019? I would feel that was a memory of betrayal rather that a positive attribute, and prefer to let it slide from memory, maybe chant something related to an area where he did visibly fight for what I'd voted and care about.

So why are his supporters adopting that as a "lead" chant at rallies, and not chanting something else - anything else - to avoid focus on such a visibly broken promise from his past election that is fairly clearly, gone nowhere, going nowhere now, apparently was never seriously intended to go anywhere once it got him elected, and virtually certainly is going nowhere in future even if re-elected?

Two Minutes Hate

People loved chanting "lock her up". So why should they stop? In some sense, that's why no effort has been made - actually locking up Clinton, or trying to, would detract from the purity of hating her and everything she represents.

But what about Trump's supporters? They can see these things too

I put it to you that they can't, don't or won't. They're watching a different set of news channels, pundits, and talk radio to you. They're not interested in having their prejudices unconfirmed.

That's how the culture war operates. It's entirely symbolic. People who have bought into it fundamentally aren't interested in the underlying messy reality. After all, Clinton hasn't done anything personally to them. She hasn't even been responsible for any particular policy the hatred rallies around. What they hate is what Clinton represents.

That's why they don't care about "outcomes". Offending liberals is the desired outcome.

When elected, Trump made a big point that his opponent should be investigated and "locked up" over the email controversy. Almost immediately after winning the election, he made tacitly clear he was dropping that as a serious proposal, and to the best of my knowledge he did in fact drop it.

Your entire premise is wrong. Trump has and continues to see this as a serious proposal:

In November of 2018, the NY Times reported that Trump Wanted to Order Justice Dept. to Prosecute Comey and Clinton.

President Trump told the White House counsel in the spring that he wanted to order the Justice Department to prosecute two of his political adversaries: his 2016 challenger, Hillary Clinton, and the former F.B.I. director James B. Comey, according to two people familiar with the conversation

...

Mr. Trump repeatedly pressed Justice Department officials about the status of Clinton-related investigations, including Mr. Whitaker when he was the chief of staff to Attorney General Jeff Sessions, according to a person with direct knowledge of the conversations

This was soon corroborated by CNN: Trump raised prosecuting Clinton with top White House, Justice officials:

President Donald Trump on multiple occasions raised with Deputy Attorney General Rod Rosenstein and Matt Whitaker, who was then-chief of staff to Jeff Sessions, whether the Justice Department was progressing in investigating Hillary Clinton, according to a source familiar with the matter.

The President also wanted his previous White House counsel, Don McGahn, to ask the Justice Department to prosecute Clinton on numerous occasions, but McGahn rebuffed doing that, the source said.

The Mueller report, released in April 2019, appears to confirm this reporting (page 321 of this huge PDF, or Part 2 Page 109):

Later in 2017, the President continued to urge Sessions to reverse his recusal from campaign-related investigations and considered replacing Sessions with an Attorney General who would not be recused.

On October 16, 2017, the President met privately with Sessions and said that the Department of Justice was not investigating individuals and events that the President thought the Department should be investigating. According to contemporaneous notes taken by Porter, who was at the meeting, the President mentioned Clinton's emails and said, "Don't have to tell us, just take [a] look." Sessions did not offer any assurances or promises to the President that the Department of Justice would comply with that request. Two days later, on October 18, 2017, the President tweeted, "Wow, FBI confirms report that James Comey drafted letter exonerating Crooked Hillary Clinton long before investigation was complete. Many people not interviewed, including Clinton herself. Comey stated under oath that he didn't do this-obviously a fix? Where is Justice Dept?" On October 29, 2017, the President tweeted that there was "ANGER & UNITY" over a "lack of investigation" of Clinton and "the Comey fix," and concluded: "DO SOMETHING!"

The fact that Trump was unsuccessful in his efforts says more about the (lack of) evidence than it does about Trump's desire to pursue this campaign promise.

Now in early 2018, then-Attorney General Jeff Sessions declined to appoint a special counsel, but did assign a US prosecutor to investigate several Clinton-related matters:

“I have already directed senior federal prosecutors to evaluate certain issues previously raised by the Committee,” Sessions noted, referring to a November letter to Congress that provided vague suggestions that he would consider congressional GOP complaints about the Clinton investigation.

If you read the original letter sent by the committee, you can see they're talking largely about Clinton's emails, the Clinton Foundation, and Clinton's (supposed) involvement in the sale of Uranium One.

We have not yet seen any results of this investigation.

Additional related articles:

• Trump Is Going on the Offensive to Take Down His Political Enemies

A large part of the problem here is that you are viewing the chanters as Donald Trump supporters. Perhaps that's not how they view themselves. Perhaps they view themselves as protesters who are bringing attention to the ongoing failure of the government to enforce proper treatment of classified information.

There is an argument that Hillary Clinton should be arrested and charged. She was given classified information that she then treated recklessly and carelessly. The decision not to charge her was made by someone who himself leaked classified material.

Another observation that the chants may be less about supporting Trump and more about Clinton:

But what struck me as odd, in retrospect, was that this man was still obsessing over his hatred of Clinton, nearly two years after she lost the election. He had nothing positive to say about the man he’d voted for, only wrath for the woman who ran against him.

Really though, if you want the answer to this, we're the wrong place to ask. Go to a Trump rally, find a chanter, and ask that person. Repeat until you get a nice selection of answers with many repeats. The only thing we could really do would be to link you to someone else who did that. But it seems like the media is more interested in speculating than in doing actual research, as I can't find anything like that.

It's a bit of a sunk cost fallacy, or escalation of commitment.

Escalation of commitment is a human behavior pattern in which an individual or group facing increasingly negative outcomes from a decision, action, or investment nevertheless continues the behavior instead of altering course. The actor maintains behaviors that are irrational, but align with previous decisions and actions.

A non-trivial number of people bought into the idea of trial-by-political-rally that Republicans started in July 2016. In the time since, a Republican controlled House and Senate, and later Justice Department, were unable to find anything with which they could get charges filed against her (and certainly not for lack of trying).

Instead, a number of prominent people under Trump have been found guilty of federal crimes, and if not for the Justice Department's policy against indicting a sitting president, Donald Trump would likely have been indicted by now as hundreds of former federal prosecutes have come out to claim.

So what's a person in this situation to do? Unfortunately, many humans are remarkably resistant to admitting they have been duped. By some estimates, less than 5% of financial scams are ever reported because people are too ashamed to admit they were tricked, and that's when money has been taken from them. While some might snap out of it, many people will instead double-down on it, even as it continues to look more absurd, because they are already in too deep for their pride.

Looking at Politico Article from March, a month or so after the appointment of Barr as Attorney General, it seems likely that the re-emergence of "Lock Her Up" is linked to the same drain the swamp narrative used by the Trump campaign in 2016. I expect if he's ever asked about it directly he'll lay blame on Democrats for blocking investigations into Hillary Clinton.

The opening paragraph;

President Donald Trump said in an interview that aired Friday he hopes Attorney General William Barr will “do what’s fair” with regards to opening investigations to perceived crimes by his 2016 opponent Hillary Clinton, former FBI Director James Comey, former intelligence chief James Clapper and former CIA Director John Brennan.

This plays into Trumps repeated comments about the Russia investigation as a Witch Hunt and the "Crooked Dems" positioning. By suggesting he's asking for "fairness" it paints anyone who disagrees with him as "unfair". Given the Democrat control of the house of Representatives and the subsequent difficulty of a Republican President to promote their own agenda it seems likely this will build toward the same plan as 2016.