In addition to being pointedly not invited to McCain's funeral and memorial service - where former presidents Barack Obama and George W. Bush will both eulogise the Arizona Republican - Trump was quietly asked to stay away from former first lady Barbara Bush's funeral earlier this year.
He also opted to skip the annual Kennedy Centre Honours last year amid a political backlash from some of the honourees, and has faced repeated public rebuffs from athletes invited to the White House after winning championships.
"We're not talking about a president going and having a rally in a state that voted against him," said Tim Naftali, a presidential historian at New York University who previously served as the director of the Richard Nixon Presidential Library and Museum.
"We're talking about a president who can't even go and participate in a ritual where presidents are usually welcomed, and that is one of the consequences of his having defined the presidency in a sectarian way."
Trump's bitter feelings towards McCain came to dominate the first 48 hours after McCain's death, as the President ignored repeated entreaties to offer any thoughts on McCain and flew the flag above the White House at full-staff for much of the day yesterday.
He ultimately, and grudgingly, caved to public and private pressure and issued an official proclamation to lower the flag in honour of McCain's death.
"Despite our differences on policy and politics, I respect Senator John McCain's service to our country and, in his honour, have signed a proclamation to fly the flag of the United States at half-staff until the day of his interment," Trump said in a statement.
Trump's conspicuous absences at both McCain and Barbara Bush's funerals offer perhaps the starkest examples of the ways in which Trump finds himself ostracised from some of the duties other presidents performed as almost de facto aspects of their job.
"It is a tearing of the fabric of the presidency that he's not invited, but I understand why he's not invited because he's personalised the presidency in a way no previous occupant of the presidency has done," Naftali said.
"Donald Trump has never accepted the fact that he is the head of state."
A senior White House official rejected the notion of Trump as persona non grata, saying for example that it is not the norm for sitting presidents to attend the funerals of former first ladies, in part because of disruption it causes.
Obama, for instance, did not attend the funeral of former first ladies Betty Ford or Nancy Reagan when he was in office. Instead, Michelle Obama went in his place, much as Melania Trump attended Barbara Bush's funeral.
The official added that Trump has hosted and attended events not in line with traditional Republican orthodoxy, and specifically pointed to his various meetings with labour unions soon after taking office, as well as his attendance at the opening of the Mississippi Civil Rights Museum last year despite controversy surrounding his visit.
Yet Trump has also found himself excluded from - or opting out of - other, more routine parts of the presidency.
When he visited the United Kingdom in June, his visit with the Queen was undermined by reports in the British press that she was the only member of the royal family willing to meet Trump. And two months earlier, the President notably did not receive an invitation to Prince Harry and Meghan Markle's wedding, though the duo - who are reportedly no fans of Trump - eschewed nearly all political guests.
Trump also skipped last year's Kennedy Centre Honours after three of the five honourees said they either would or might boycott the traditional White House reception pegged to the celebration. And Trump has faced high-profile rebellions from athletes he'd hoped to honour.
In June, for example, the President hastily disinvited the entire Philadelphia Eagles from a White House event in honour of their Super Bowl championship after growing frustrated that, in protest at some of his policies, the team had planned to send only a small delegation of players. The party went on, sort of, albeit without the guests of honour.
Previous presidents have also dealt with defectors, of course, and a number of athletes and teams have still visited Washington to be feted by Trump.
In many cases, the rejection is mutual. Trump - who prefers the comforts of his Trump-branded resorts and restaurants - rarely ventures far from his cosseted bubble. He is generally uncomfortable crossing into hostile territory, and prefers to frequent places where he is likely to be lauded, rather than rebuked.
"We've kind of elected this apex predator, and you don't sit T-Rex down at the dinner table," said Alex Castellanos, a Republican media consultant and strategist. "I think civilised society doesn't want him behaving crudely at the dinner table, and he has no interest in their pretensions."
At his recent rallies, Trump has taken to expounding on his lack of acceptance by the so-called "elites," proclaiming it as a badge of pride. And his disdain for what he terms political correctness is similarly applauded by many of his supporters.
"The thing to realise is that Donald Trump's base revels in him playing the transgressive jerk," said Rick Wilson, author of Everything Trump Touches Dies and a veteran of Republican campaigns.
Wilson added that with McCain in particular, the funeral snub perhaps stings more than most, in part because Trump can't abide not being the main focus of adulation.
"You know what is making Donald Trump the craziest right now is he's not the centre of attention," Wilson said. "He's crawling the damn walls because they're running story after story on John McCain and he hates it because he's not the centre of attention."
Trump also has sometimes struggled in the role of consoler-in-chief, another key demand of the presidency.
When he visited hurricane-ravaged Puerto Rico last year, he drew widespread scorn for describing his trip as "lovely" and tossing paper towels into the crowd as if shooting baskets, even as his Administration struggled to cope with the deadly tragedy.
He came under condemnation again this year when, during a listening session for those affected by the Parkland school massacre, he held note cards with a basic reminder of emotional empathy printed in black Sharpie: "I hear you."
Andrew Card, chief of staff under President George W. Bush, said he struggles with the current political climate in part because he was raised to believe the president, whoever he or she is, is deserving of respect, and that he thinks both sides are to blame.
"When the President doesn't appear welcoming, it's his problem, he's created a problem," Card said. "When others refuse to accept an invitation, I think that's wrong."
But, he added, a paradox is that Trump in many ways has created the very environment he now chafes against. "I do think the President gives permission for what I would consider to be rude behaviour," Card said, "and yet he reacts so poorly to other people's rude behaviour."
