The humiliating exit from the Capital One Cup at the hands of League Two side Bradford on Tuesday night may become a critical moment in Wenger's reign, especially with the Gunners also misfiring in the Premier League.
Wenger insisted that part of his job is to help the team "recover and focus on the next game", but the Arsenal Supporters' Trust (AST) was set to demand immediate changes at a meeting tonight with chief executive Ivan Gazidis.
The AST has long supported the Gunners' prudent financial approach but believes the lack of spending has now gone too far and that the defeat by Bradford was a symbolic moment, with the team having decreased in quality year after year since 2009.
The Trust wants changes at board level, for Wenger to release some of his duties to others and for the manager to spend some of the many millions available to him.
AST spokesman Tim Payton said: "This is the most difficult time in Arsene's 16 years and both the club and himself need to change direction quickly if his wonderful era is not to end on a sad note.
"The Arsenal Supporters' Trust cannot fathom why £70million was left untouched this summer. Arsene needs to get over his distaste for spending and use the resources that, after all, are provided by the hard-pressed fans who watch the team.
"The AST believe a shake-up is needed. We would like to see new, younger blood added to the board, and they also need to exercise more control and direction over Arsene's football strategy.
"One man cannot direct all transfer targets, wages, coaching methods and manage the team at games. It's too much for one man."
Even if results do not pick up, Wenger's position should be safe at least until the end of the season but an increasing worry for club executives is that significant numbers of fans are not turning up to matches at the Emirates despite having bought tickets.
There is also growing frustration that players brought in since the departures of Cesc Fabregas, Samir Nasri and Robin van Persie have failed to deliver.
Even Arsenal's honorary vice-president Lady Nina Bracewell-Smith expressed that frustration last night, saying on Twitter - though deleting it soon afterwards - that: "Gervinho is a FLOP player".
There is also a fear that Theo Walcott may also leave the club - especially with Manchester United now linked with the England forward.
Arsenal do not play now until Monday, when they face Reading away, and Wenger has to try to raise the players' spirits though he insists the team suffered some misfortune at Valley Parade.
"It's extremely disappointing because in the second half and extra-time it was one-way traffic," said Wenger.
"We created a lot of chances but the final ball was missing."
Asked how Arsenal could recover, he added: "I believe that it is part of our job to recover and to focus on the next game."