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According to fivethirtyeight.com Donald Trump's popularity seems to be rather constant over time in opposition with his predecessors Barack Obama and George W. Bush who suffered a popularity erosion quicker than the current president.

I am wondering how does he manage to maintain his popularity over time.

This article suggests that being more intuitive than analytical is an important factor in explaining his popularity:

A study published in the journal Translational Issues in Psychological
Science suggests that Donald Trump stands out amongst other
politicians, including fellow Republicans and past presidents, as
being exceptionally low in "analytic thinking."

However, this is only one dimension and I sense there are multiple factors that helps him to remain popular.

Question: How does Donald Trump manage to remain so popular?

I am particularly interested in articles or studies that provide more insight into this.

Here is one take from sociocultural anthropologist Joel Robbins.

The Mysterious Power of Arrogance, 2 FEB 2017

Why do overbearing, obnoxious people so often come out on top? What the story of a local celebrity in the remote highlands of Papua New Guinea reveals about the rise of Donald Trump to the U.S. presidency.

In the community of Urapmin lives a man named Kinimnok—a boastful, loud, and often angry public figure—whose role in society may help us understand some Americans’ love of those who are supercilious and bombastic.

...

In all societies, just as with the Urapmin, people have to balance values that are not fully compatible with one another. The values that come into conflict differ—in modern democracies some of the key opposed pairs are values like security and freedom, liberty and equality, and the self and the community—but the trick of balancing them remains much the same. Hence, people like Kinimnok, who give up on balance and put all their efforts into achieving a single value, always stand out from the rest, and they often seem to captivate their fellows.

A certain kind of rugged, me-and-mine-first individualism has long been a value in the United States, but it has competed with other values that are concerned with openness, tolerance, and the common good. People usually balance these, compromising on all of them in order to realize a little bit of each. But perhaps because the value of individualism has become harder for most people to realize, even partially, in their current economic circumstances, many Americans recently proved captivated by someone with little interest in values other than individualistic self-promotion. They were joined to a candidate—who went on to become President Donald Trump—by a bond anchored in his ability to express this one value of theirs very fully.

Societies tend to work better when their members struggle to balance conflicting values, and this gives grounds to worry about what leadership devoted to a single value—particularly one such as self-promotion—might be like. Based on my experience in Papua New Guinea, I am not as surprised as I once would have been that many people in the U.S. found themselves attracted to someone who single-mindedly pursues one of their values at the expense of all the rest. But the Urapmin never put Kinimnok at the head of their government, allowing his willfulness to do away with the role of lawfulness in their lives. It remains to be seen how America’s other values will fare in the wake of an election that prioritized one value above the rest.

One of the issues mentioned in this article is compromise.

In 1988, George H. W. Bush said "Read my lips: no new taxes." His popularity with Republicans soared. After a compromise with Democrats in Congress, that resulted in increased taxes, he lost his re-election bid.

President Trump has shown no willingness to compromise; going so far as to attempt repeated end runs around Congress. As long as he continues with that approach, it appears that his popularity (with his base) will remain steady.

It's actually surprising hard to find surveys that also ask the "why" question of the supporters. I did find one on-line survey by "SuveyMonkey", although I'm not sure of its reliability; even the date is unclear. It used open ended questions.

a large majority of Republicans (85%) approve of the job Trump is doing as president. When asked why, they highlight that he has “kept promises” made during the campaign, “put America first,” “tried to get things done,” and “reversed the last eight years” of Obama administration policies.

Many respondents cite specific campaign slogans (“MAKE AMERICA GREAT AGAIN!” in some form or another is used by about 8% of all respondents) in their responses.

As the chart above shows, college grads tend to zero in on more tangible goals (top mentioned topic was “reduced regulations”) whereas those without college degrees focus on vaguer ambitions like “making America great again.” Many college grads applaud Trump for “reinvigorating the economy” by removing “intrusive” regulations on business that do more harm than good. This group also advocates another time-tested Trumpism: “Draining the Swamp.” However, the college grads who cited this reason for approving of Trump also acknowledged that while Trump is “trying” to drain the swamp and accomplish his other campaign promises, he is “being blocked by others,” including both Democrats and members of his own party.

One topic that emerged equally from non-college grads and college grads was the feeling that while Trump has “good positions,” he also has a “flawed personality” that does not lend itself to effective communicating or strategizing.

On the other hand, those with less than a college degree praise Trump using some of his more amorphous campaign slogans: “Making America Great Again” and “Putting America First.” These supporters also appreciate Trump for his plain-speaking (“Tells it like it is”) and for the fact that he is “doing his best” despite facing adversity.

There are a lot of papers that try to profile his supporters in one aspect or another, but that's perhaps too long to go over here

The US economy is doing quite well lately, and unemployment, especially among minorities, is at record lows.

That is a good reason to be popular, especially if one was previously unemployed.

How does Donald Trump manage to remain so popular over a rather long period of time?

Because in the eyes of many, he says the things that need to be said. And tries to do the things that need to be done.

So it's not unsurprising that in the eyes of those, he's still popular.