Absolutely should stay.
Stu, you mention a time when he bought bergkamp, henry etc. All inspired signings from Wenger, and all on a budget. However in today's game, if Wenger is interested in a player today, then you can guarantee City, Chelsea, United will be looking too. Arsenal were the club first interested in Mata, Hazard, Ageuro, and I'm sure there are other, similar instances. From that point Wenger cannot win, Arsenal can't compete financially in a bidding war for these players, and thusly Wenger is forced to operate in a different manner.
He does so and does so sustainably, in accordance with FFP rules.
If he is guilty of anything it is that football has moved on, and his methods are out dated. However with FFP coming in, I think he is the man to get Arsenal back up there.
In recent years he has been unfortunate with player loyalty (Fabregas, Nasri and RVP left within a 12 month period and you CANNOT just simply replace these players). Clearly there has been a hangover from this.
Clubs go in cycles, you can't have success year upon year. However look at what Wenger has achieved at Arsenal, he's made them one of the biggest clubs in Europe overseen the transition into a Magnificent stadium. If they sack him then they lose one of the most experienced and proven managers in world football. I'm sure Real Madrid will be happy to have him.