Everybody seems to think Wenger is the one who is being stubborn and doesn't want to change his ways, but wasn't it reported this summer he was at loggerheads with the board about the level of ambition/investment? Apparently he felt the club's wage structure didn't allow it to compete with Chelsea and the Man U clubs for the signings he wanted to bring in, and he wasn't willing to pay over the odds for players like Cahill whom he perceived as overpriced and overrated.
It appears to me that for some reason or another Arsenal have been extremely frugal in recent seasons despite vastly increasing their crowds and probably revenue, and in today's football world you can only go so far without significant investment.
Perhaps Wenger's "problem" is that he would rather develop players he believes have the potential to be world class but are not quite ready yet (and get poached once they are) than to bring in established players who are decent Premiership players but not quite good enough in his mind to take the club forward. If given the choice to spend more and have a real go at the Premiership title I don't doubt for a second he would take it, and I don't think there would be many better managers to make it happen too...