I doubt they would axe it, because A) it's too popular, B) it's worth a lot of money in licencing (both programme format to other channels worldwide and in merchandising) and C) because they axed it before, only for Channel5 to snap up the presenters and production team and produce a car programme while the BBC had no competition.
They would think twice about making that mistake again (although they might not have learnt).
Jonathan Ross wasn't technically axed. His contract ended and because of the controversy and his huge fee, the BBC decided not to renew his contract.
Clarkson isn't paid as much as Ross.
The TG budget has already been cut, that's why the series' are only 6 episodes now. They decided they would rather continue with the same size budget per episode but fewer episodes per series, than have more episodes with less spent on each.
Granted I think it does need a review of how it's spending the money, more stuff shot in the UK (eg: you don't need to go to Italy to film 3 hot hatches, there are some great roads in the UK) and so on.
And yes after 10 years it does need a little refresh, but what would you do to do that, whilst still keeping the bits everyone loves?
