He may not have a choice, if enough MPs complain to the Chairman of the 1922 committee, they can instigate a 'no confidence' vote.
I suspect it will all hang on the results of the Shropshire by election. If the conservatives lose, and there is actually a chance that they might, he will be out of the job by the weekend. I think that will apply also if the conservative wins with a very narrow majoirty.
So everyone. Th e man seriously challenging, what I understand is a lack-lustre candidate, helicoptered in, is the LibDem candidate, so anything anyone can do to support him, could be hammering the last nail in BJ's political coffin and he will be able to resign his current post to spend more time with his burgeoning family.