It is hard to imagine a bleaker matchday scenario for Arsène Wenger's Arsenal than defeat to a fourth-tier opponent that has been pieced together on a shoestring. The League Cup quarter-final defeat at Bradford City on the stereotypical Tuesday night up north represented humiliation or, in the words of one brilliant headline, "Brad Pits".

And yet, the true measure of Gooner despair was that it was not actually so wildly unpredictable or shocking. Any regular Arsenal watcher has seen the fragility of this team, the China-doll brittleness, which hints at calamity around any corner. Even in victory at present, such as Saturday's home win over West Bromwich Albion, the post-match emotion for anybody connected to the club can major on relief and the aversion of crisis.

Arsenal are not so much on the back foot these days as mired in ever-decreasing circles of anxiety and frustration. It is deeply unsettling. They are football's version of the soap opera with lots of shouting and the plot-lines have become wearingly repetitive.

Wenger has enjoyed glorious success at the club and, therefore, he knows what it takes. And so he keeps doing it. As he has grown older, he has become more stubborn, more determined to prove that his way is the right way. And so he keeps pushing it, promoting it, with ever more zeal.

But Arsenal have drifted. From being title winners and, generally, contenders under his charge, they have become also-rans. The limit of the expectation level is the top four, Champions League qualification – and the competition, in which Arsenal always advance to the knockout stage, offers hope, reassurance, even the mirage of the ultimate triumph. Is it enough?

Wenger can be seen as the Sideshow Bob character in the Simpsons clip who steps on the rakes and, after each defeat against opposition that his teams would, in years gone by, have swatted aside, the questions recur. We have heard them countless times but they distil into one: Is Wenger, and the approach that he has entwined with the club's DNA, right for the future?

Where once it would have been sacrilegious to suggest that Wenger should go, it is now a nagging discussion topic. And yet, part of the angst, part of the dizzying carousel is that, in practical terms, at least for the remainder of the season, it is a non-discussion.

Arsenal do not intend to sack Wenger and Wenger does not intend to quit. He has said, repeatedly, that he always honours his contracts and his current one takes him to the end of next season. Ivan Gazidis, the chief executive, who runs the club on a daily basis on behalf of the majority shareholder, Stan Kroenke, is hugely supportive of and sympathetic to Wenger. He believes in him; their ideology, their principles, their vision of the club as a self-sustaining business off the field and a stylish, distinctive team on it, are the same.

Gazidis' commercial strategy is built on the exploitation of untapped markets, particularly in east Asia, and he hopes to tempt supporters in the region to buy into the club on an emotional and more literal level. The concepts are linked. Gazidis will tell you that for the fan in, say, China, the notion of what Arsenal stand for (attractive football, excitement, loyalty, aspiration, fighting spirit etc) is fundamental.

As they identify with that, so they are more likely to part with their cash to sign up to the club's in-house media channels or other, associated money-making outlets. And at the heart of everything is Wenger. This is not to say that a new manager could not come to embrace and symbolise such values; merely to illustrate the complications of a potential parting with Wenger.

The pro-Wenger argument also asks who, realistically, could be brought in to successfully re-energise the club's fortunes and whether Wenger is not the best man to fire the upturn. He did it last season, after arguably his lowest ebb – the 8-2 loss at Manchester United, which compounded the summer from hell in the transfer market.

It is worth noting, too, that Arsenal's travelling fans chorused Wenger's name after Bradford had taken the lead at Valley Parade, in response to the taunt from the home crowd that he was "getting sacked in the morning".

The 4,500 that made the trip on an inclement school night are the true barometer of support, more so than the internet and phone-in angries.

Wenger, though, is becoming increasingly angry and obtuse; more and more at odds with his image of cool sophistication. In Athens last week, before the Champions League tie against Olympiakos and in the wake of the damaging home defeat to Swansea City, he was aggressive and confrontational, as he took issue with media pundits and newspaper stories about a furious post-Swansea dressing-room inquest. At half-time against Bradford he tore into his underachieving players. The worry concerns whether they are still listening.

The broader issues endure: the reluctance to splash the serious cash that is available in the transfer market; the mismanaged wage bill; the loss of top stars. There have even been questions asked about Wenger's recent record with regard to player purchases, which was once his personal fiefdom. Gervinho's performance at Bradford offered rounds of ammunition to the critics.

Supporters hope that January will bring reinforcements of quality. Klaas-Jan Huntelaar, Demba Ba and Wilfried Zaha are prominent on the list of permanent targets while Thierry Henry should return on a second short-term loan.

Wenger's desperate quest for solutions saw him field an almost full-strength team at Bradford in a competition that he has long been sniffy about. Yet the break from policy only intensified the dejection and the sense of helplessness.

With the external pressure relentless and close to unbearable, it is easy to fear that Wenger is in the throes of the end game. He does not accept it and he will keep fighting, keep on doing his thing. He and Arsenal lurch on.