What’s more, the Rat Pack was breaking up, he was being hounded by the FBI over his mafia connections and his 1966 marriage to Mia Farrow was already on the rocks.
When a Las Vegas casino decided it wasn’t going to extend him any more credit, Sinatra stormed out, found a golf cart, pushed Farrow into it beside him then drove it through the hotel’s front window.
The manager responded by punching the caps off the singer’s teeth with one clean right hook.
The resulting headlines were humiliating to say the least.
“Kid,” Sinatra told Anka, “I’m fed up. I’m going to do one more album, and I’m out of here.”
Anka was distraught at the idea that his musical hero might be ready to throw in the towel.
He returned to his home in New York determined to produce a valedictory lyric worthy of the great man’s status.
He already knew the song he would put the words to.
While holidaying in the south of France a year earlier, he had heard a pop hit called Comme D’Habitude (As Usual) and had been so taken by the tune that he had acquired the rights to rewrite an English version.
“At one o’clock in the morning, I sat down at an old IBM electric typewriter and said, ‘If Frank were writing this, what would he say?’ ” Anka once recalled.
“And I started, metaphorically, ‘And now the end is near’. I read a lot of periodicals and I noticed everything was ‘my this’ and ‘my that’. We were in the ‘me generation’ and Frank became the guy for me to use to say that. I used words I would never use, ‘I ate it up and spit it out’. But that’s the way he talked.”
The result, of course, was My Way, one of the greatest popular songs ever to grace a hit parade.
It entered the UK charts 50 years ago this month and remained in the Top 100 for 124 weeks, a recordbreaking 75 of those in the Top 40.
It has since gone down in history as such a classic that it has been covered by more than 100 artists, from Elvis Presley to Sid Vicious, and is said to be requested for funerals more than any other track.
But, if a French pop star had not been jilted by a teenage beauty, the song might never have seen the light of day.
As it was, when Claude François was dumped by France Gall – the blonde beauty who won the Eurovision Song Contest in 1965 – he teamed up with a composer called Jacques Revaux to write a mournful ballad to lost love.
Entitled Comme D’Habitude, it was the very song that Anka was so taken by when he saw it performed on TV while in France.
In fact, Anka was not the first person in the music business to spot its potential.
Ken Pitt, a manager, had been so taken by it that he had asked a jobbing songwriter called David Jones to write some lyrics.
Jones went on to earn superstar status as David Bowie but he later admitted the words for Revaux’s classic melody that he handed in to Pitt were lame to say the least.
“I turned in the pitifully awful title Even A Fool Learns To Love which he rejected out of hand, quite rightly,” Bowie recalled in 1999.
Anka’s version, however, was an instant hit thanks to a phenomenal performance by Sinatra.
One critic described it as “hypnotic, masterly in its slowbuilding defiance, and proud rather than blustery”.
While My Way never made No 1, its lyrical power and musical distinction did not go unrecognised by Sinatra’s peers, hence the raft of cover versions over the years.
Pistols’ Sid Vicious Nina Simone, Glenn Campbell and Aretha Franklin all recorded versions and it was the first Elvis Presley single to be released after his death.
In Britain, the song was performed by stars such as Sir Tom Jones, Dame Vera Lynn, Dorothy Squires and Shirley Bassey, who was the first female artist to swap “man” for “woman”.
But perhaps the most famous rendition of the song after Sinatra’s was the version recorded by the Sex Pistols’ Sid Vicious for the 1978 cult movie The Great Rock ‘N’ Roll Swindle.
Filming was done at the Olympia Theatre and Vicious made his entrance descending an old-school, lit-up staircase.
His snarling rendition, performed to an audience of men in black ties and women in ball gowns and pearls, ends with him taking a handgun from the pocket of his white tuxedo and shooting several members of the audience.
A rebel to the last, he died of a heroin overdose 10 months later.
But you don’t have to be a megastar to perform My Way.
It has become one of the most popular hits at karaoke bars worldwide.
Even our very own former prime minister David Cameron likes to perform it after a few glasses of wine, according to a 2012 biography.
But one country where it is probably best avoided is the Philippines.
There, anyone who performs it is dicing with death.
In the decade following the millennium, at least a dozen people were killed after offkey renditions of Sinatra’s classic – so many that the Press introduced a subcategory of murders known as the “My Way killings”.
Butch Albarracin, owner of Center for Pop, a Manila-based singing school that has propelled many artistes to stardom, has his own theory about why the song sparks such aggression.
“The lyrics evoke feelings of pride and arrogance in the singer, as if you’re somebody when you’re really nobody. It covers up your failures. That’s why it leads to fights.”
Whatever the underlying cause, many Filipino karaoke bars have removed the song from their playlist and amateur crooners with a well-founded sense of self-preservation stick to less iconic numbers.
Elsewhere it retains its evergreen appeal to this day.
Not surprisingly, perhaps, Donald Trump – not a man who could ever be accused of being backward in coming forward – wanted Anka to perform the song at his inauguration but the songwriter was going through a divorce at the time and passed on the opportunity.
Instead, the Donald had to settle for a rendition by Nashville-based jazz singer Erin Boheme, who sang it for the awkward first dance he and wife Melania performed at his inaugural ball.
When asked what her father would think about the 45th president choosing his theme song for the occasion, Nancy Sinatra tweeted: “Just remember the first line of the song, ‘And now the end is near’.”
Ironically, her father, the man who was so instrumental in spawning the My Way phenomenon, would rail against it in later life.
“Every time I get up to sing that song, I grit my teeth,” Sinatra once said, “because no matter what the image may seem to be, I hate boastfulness in others. I hate immodesty.”
And when he died, the number they played at his funeral was not the undertakers’ favourite but the ballad he considered his theme song, Put Your Dreams Away.