Now the talk is about trying to find someone to replace him.
“I can’t see a great deal of longevity in his career unless he gets a big score that makes him feel it’s worth carrying on,” said Graeme Swann, the former England off-spinner who knows him well.
After Cook was caught-and-bowled by Josh Hazlewood for 14 on day four at the WACA, which England closed on 132-4 in their second innings, 127 adrift, some were suggesting that it is not only the Ashes that are gone – but the former England captain too.
We have, of course, been here before – quite a few times, in fact.
As Nasser Hussain, the former England captain and one of Cook’s greatest supporters said prior to the Perth Test, “one thing the last 10 to 12 years have taught me is that whether it be his captaincy or his batting, you are a fool to write off Alastair Cook; you do so at your peril.”
At the same time, the statistics tell a suggestive story: scores in this series of 2, 7, 37, 16, 7 and 14 are unbecoming of one of the best batsmen that England have had, a man who has given the proverbial blood, sweat and tears since his debut at Nagpur in 2006.
That this is Cook’s 150th Test only adds poignancy to his predicament.
We are reminded by that very figure what a magnificent servant he has been and the consistency he has displayed.
Cook is England’s highest Test run-scorer, an unusually determined, no-frills batsman who, like Geoffrey Boycott, has often been cited as someone that you would want to bat for your life.
At present, however, you would perhaps not be too confident of being around for much longer if Cook was all that stood between you and the Grim Reaper.
As Cook walked off at the WACA yesterday, having popped back a return catch that he would surely not have offered in his prime, his future was once more under the microscope.
Mitchell Johnson, the former Australia pace bowler, had ramped up the pressure prior to the match by saying that he thinks that Cook is “on his last tour”.
“He definitely does not have that look of determination in his eye, that desire,” said Johnson. “I don’t see that fire in his belly any more… I would be surprised if he went on much longer.”
According to Swann, though, Cook “still wants it” and is “still trying to do desperately well”.
“I still sense Cook has that burning desire,” he added. “He’s just in horror nick.”
Although clearly fighting himself and his footwork, Cook would not be human if he had not lost a little of his previous edge.
It is never easy for a captain to return to the ranks, while for all the fact that he has spent much of his career dealing in high numbers, Cook has never been covetous of personal milestones.
“I wonder what drives him now, what keeps his mind stimulated,” mused former England batsman Ebony Rainford-Brent on Test Match Special.
“I wonder if he still has that hunger and drive. It’s been a bad series for Cook, but I can’t see a viable alternative.”
And there, in a nutshell, is the heart of the matter. For where is the alternative to the great left-hander?
Ever since Andrew Strauss retired in 2012, England have picked and dispensed with so many opening partners for Cook that you can barely keep up with them, Mark Stoneman the latest to sup from the poisoned chalice.
There are some quality candidates out there, be they from the list of the already tried and tested to others playing county cricket, but would they do any better than a man who is hardly ancient in sporting terms; Cook only turns 33 on Christmas Day.
Would they have coped any better with the hostility of Mitchell Starc, Pat Cummins and Hazlewood in this series, or more competently with the wiles of spinner Nathan Lyon?
Cook, you sense, is as likely to find his run-scoring form again next summer as anyone who dared to fill his boots.
It was only a few short months ago that he scored 243 against West Indies, a rather different standard of opposition, perhaps, but the sort of score that many of Cook’s discarded opening partners would have killed for.
That innings, however, is starting to look more like the exception than the rule.
It is the only time, in fact, that Cook has passed fifty in his last 14 Test innings, and the only time that he has reached three figures in his last 27 Test innings.
Time waits for no man, and although Cook is still in excellent physical condition, perhaps the mental aspect of playing, captaining and everything else that goes with it has taken its toll.
In Test match terms, he has got an awful lot of miles on the clock. Ultimately, only Cook will know his own mind and when the time is right to call it a day.
He deserves the right to go out on his own terms, even if international sport is rarely so understanding.
Prior to this series, Lyon talked fatuously of “ending careers”. Whether Cook’s is one of them remains to be seen, or perhaps England’s great fighter will carry on fighting.