They aren't going to find a replacement in January; who's going there, especially if they struggle? They knew all along we wanted him and could have been looking months ago. Everyone already knows he's unhappy -- him acting out doesn't change anything and only damages him. I know he has the rep as being volatile, but my guess is he pulls a Milner and keeps his head down instead. He isn't going AWOL like Tevez.
They don't need to find a world class replacement, and there's always someone on the market in January, particularly in a world cup year, there'll be a fringe player fro some major international team who can't sit out all season - and before you say Sanchez is in the same boat, he's not, he could go on holiday until July and he'd start for Chile.
Also him acting out doesn't damage him at all. Pep knows him, and Sanchez knows we desperately want him, that sin't going to change, and every time he's acted out so far more and more balm just gets dumped on wenger for keeping him.