At a rather dismaying rate, the accumulating evidence suggests that indeed he has.
Consider again, for starters, his delusional reaction to a third straight undressing of his team by an outfit at the serious end of the title race, and the second time Chelsea have done it with a killing instinct bordering on contempt.
"We had mountains of possession," announced Wenger. "We were not running after the ball for 90 minutes. We were not in a position where we were dominated. We were always in an attacking position. I'm completely happy with the performance and the spirit. When we got into it we were completely dominant."
Unfortunately, when Arsenal did get into it there really wasn't a whole lot to get into, other than fresh evidence that beautiful football without a cutting edge is like most other forms of foreplay. It needs, well, a result.
Arsenal, as currently constructed in the critical absence of Robin van Persie, suggest that against the likes of Chelsea and Manchester United they might experience difficulty scoring in a dodgy massage parlour.
A harsh point, maybe, but inevitable when you consider that in 180 minutes of utterly pivotal action against Chelsea they have failed to find the net while conceding five goals.
Though it is true Arsenal suffered a harsh fate at Old Trafford early in the season, the fact is that they were not so much beaten as eviscerated by United just a week before this latest evidence that when the heat is on the gossamer touch of the Gunners simply goes up in smoke.
Yes, it is true Arsenal threaded their way towards Peter Cech's goal for most of the way. But it was tortuous work.
Long before the end of the transfer window it was clear that the admirable Andrei Arshavin was wilting under the pressure of trying to lead the attack. He is a brilliant football artist but when Van Persie was struck down even those on a much lower plane of football intellect than Wenger could trumpet the wisdom that Arsenal needed a bigger horse than even the most gifted of Shetland ponies.
Talking of intellect, the most telling indictment against Wenger is maybe that in his current situation he has carried rather too much of the arrogance that often accompanies it. He says he had the money to make a vital signing up front, but not the instinct. Why not? We have to guess that it was because it might have offended his own sense of omnipotence, his belief that, one way or another, he had built the resources to deal with any situation.
Heaven knows, it is a beguiling idea. Imagine the anointing of Wenger that would have inevitably followed some freakish achievement by Arshavin, some consistent reproduction of the brilliance which confounded Liverpool at Anfield recently.
Yet on Sunday Arshavin might have been a mere charm on a bracelet worn by Didier Drogba. The decisive power and judgement of the Chelsea striker, admittedly now pretty much in a class of his own as a pure finisher, settled the match and, let's be honest, the debate centring on Wenger's resolution to do it entirely his way.
He has tried to do this for some years and anyone who loves the artistry of the game is in his debt. But if the old gridiron legend Vince Lombardi was wrong to say that winning is the only thing that matters, it will always be the central purpose of any competitive sport. Playing prettily, as Arsenal did on Sunday for so much of the time, without the serious expectation of a decisive end product, is at the finish an exercise in futility.
Down the years the fans of Arsenal have had plenty of reasons to believe they have inherited the football world – the beauty of Thierry Henry, the titles, the unbeaten season – but then you get used to such a banquet. It shapes your appetite. It creates a certain hunger. Wenger has to recognise some time soon that it is one that needs to be appeased. You cannot do it with a team that has become a tease.
Capello right to draw a line under sorry Terry saga
Now we are told that it was not enough for Fabio Capello to deal so swiftly and so unequivocally with the John Terry affair. Now he has to explain himself. He is right to shrug his shoulders and walk away.
Capello did, demonstrably, what he had to do. It wasn't to act as some demonic vigilante tracking down sexual impropriety; still less to be the chairman of a debate on the moral decline of English football. That would have been absurd and nearly as bizarre as some of the arguments disputing his decision. Let's remind ourselves what Capello did – and what he didn't.
He removed a captain who was in the process of spending vast amounts of money in a hapless attempt to put a lid on indiscretions which had turned his life, and the affairs of the England team he was deputed to lead, into a circus so tawdry and distracting from any serious purpose it might have heaped ridicule and disbelief on the average cast of the Big Brother show.
Capello didn't make a moral statement. Just a professional assessment of the damage already caused by Terry's loss of control over not just his personal relationships but his understanding of his responsibilities as the figurehead of the England team.
The head coach simply drew a line, clearly and with splendid brevity.
Why I quit on a high after the Cresta rush
How odd but exciting it is, at this advanced stage of decay, to find oneself sharing, however briefly, a rung of the sports ladder with Matt Dawson, the man who so coolly orchestrated the unforgettable moment when Jonny Wilkinson's dropped goal won the World Cup in Sydney.
This is Dawson reflecting on his recent descent of the Cresta Run on the occasion of its 125th anniversary: "I enjoyed an adrenalin rush every bit as intense as the day we lifted the cup in Australia."
While obviously lacking a whole directory of Dawson's points of reference, I can at least confirm the thrill of the run – and also the late Sir Clement Freud's theory that it may well be the world's ultimate laxative.
This, however, isn't the point. Dawson's first run past the notorious Shuttlecock Corner was timed at 65 seconds. So was mine. The difference is that Dawson went on to go six seconds faster the next time, and then crashed out at Shuttlecock.
Naturally, I quit while I considered myself somewhat miraculously ahead, though only after, it has to be said, carefully checking every bone in my body.
Dixon on the ball as a TV pundit
Lee Dixon did nothing to damage the sense that he is emerging as arguably television's sharpest football analyst when he imposed a little insight on the execrable Merseyside derby.
While his co-panellist Garth Crooks supported amiably the popular view that rather than a game played in the most shocking and cynical way, and one which could easily have resulted in not two but half-a-dozen red cards, it was exactly the kind which the fans loved to see, Dixon kept a poker face. Then he said, "Not one pass found the right shirt – but he liked the match."
Dixon, like the trenchant Graeme Souness, is a rare and refreshing presence. He gives the impression that when he goes into the studio he does so not to milk his celebrity but to offer a hard-earned opinion. Talking heads are 10-a-penny. Thinking ones, these days, must be weighed in gold.
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