I believe that he should not. Considering the man's vast knowledge of the game of football, track record of success and the plausible alternatives, Wenger is the best man for the job.
But I like to play devil's advocate, and there is certainly an argument to be made for the manager's removal—in fact, there are several. Let's look at five reasons why Arsenal should let Arsene Wenger go.
Every Arsenal fan is aware that the club has not won a single trophy since 2005. Considering that the FA Cup is the Gunners' only realistic chance of silverware this season, that could easily become a nine-year spell without silverware at this time next season.
At a club of Arsenal's stature, that is simply unacceptable.
Because of Wenger's breathtaking success in the first nine years of his reign, the board seems quite willing to overlook the relative failure of the successive eight. But at any other top club, the Frenchman would have been sacked long ago.
Perhaps Arsenal can only end the drought by changing managers.
Last season, the fact that Arsenal started worse than at any time during the Wenger era was taken as a symbol of the club's decline. The historic 8-2 meltdown against Manchester United was the bitter symbol of their fall.
In this campaign, the Gunners did even worse.
Most worryingly, Arsenal seemed to lack the sort of killer mentality that is necessary to win tight games against inferior opposition. They seem to be making up for it now to an extent and have been bailed out somewhat by the stagnancy of their rivals.
But topping one's own ineptitude season after season is utterly unacceptable.
What has struck the most fear into Arsenal fans for the past several seasons?
The Gunners were poised to mount a title challenge during the 2010-11 season, but despite the brilliance of Cesc Fabregas and Robin van Persie, they could not keep up with Manchester United. In the end, the defense was unable to compensate for the injuries that hurt it, and the trophy cabinet remained bare.
Some of the same problems of mental weakness and tactical ineptitude bubbled back to the surface last season. But former defensive stalwart Steve Bould was supposed to stem the tide this season with his uncompromising demeanor and focus on the basics.
Despite a promising early stretch and an above-average statistical record this season, the back line has been prone to ridiculous errors that would earn a teenager a smack about the head. That is obviously unacceptable against the best teams in England.
If Arsene Wenger, a clearly attack-minded manager, cannot turn things around, perhaps Arsenal should consider someone who can.
Few managers exercise the amount of influence at their club that Arsene Wenger does. Some of that is absolutely deserved; he probably knows 10 times more about the game of football than anyone else at the club, and his success during his almost 17-year tenure merits some elevated responsibility.
But when does it become too much?
All managers are somewhat involved in their club's transfer dealings, but Wenger almost unilaterally decides which players to buy and plays a large role in negotiations.
He also seems to be entrusted with a large part of managing the club's finances. Though the board makes the final decision on when to reach into the coffers, Wenger is much more involved in financial matters than managers at other clubs, even considering his experience.
In short, the manager is so woven into the fabric of how Arsenal operates that it will be difficult to build a future without him. But it's better to plan for that reality now and phase Wenger out before his stature grows further.
For the past several years, Arsene Wenger has had an excuse for not spending more money on players the team needs in perilously thin positions: The debt incurred by the construction of the Emirates Stadium.
Still, Arsenal had plenty of money that was waiting to be invested into the team—especially considering that the club has sold its best players season after season.
But the debt is almost paid off now, and the Gunners signed a massive new £150 million sponsorship deal with Emirates Airlines a couple of months ago. Even Arsenal's chief executive Ivan Gazidis said that it would allow the club to "be more financially competitive," "pay bigger salaries" and "invest more in transfer fees."
They just might be fulfilling that second part, as the re-signing of Theo Walcott demonstrated. But once again, Arsene Wenger did not add a much-needed attacker during the January transfer window, opting instead for left-back Nacho Monreal after Kieran Gibbs got hurt.
More of the same ineffective, outdated transfer policy will not work. Unless Wenger can adapt to the realities of the transfer market, calls for his head will be somewhat justified—especially if Arsenal do not finish in the top four this season.