Writing the Telegraph article the week of the Florence speech should have been bad enough to earn Boris a sacking. The fact that he is continuing to cause problems for May tells us that he is almost certainly looking to get sacked. May should give him what he appears to want, and as soon as possible too.
Why Boris hasn’t been shown the door already is that a). she is worried this will upset enough Tory MPs that they call for her head and b). that even if this doesn’t happen, Boris will cause endless problems on the backbenches, freed from collective cabinet responsibility to say what he likes about the Brexit process and how it is going (and how he could be doing a much better job if he was prime minister, obviously).
Let’s deal with the first one there: sacking Boris will not end her premiership. I don’t think it will, even if certain powerful MPs within the party have told her so. It is an awkward time to get rid of May. The negotiations are in a strange place, for one. They should have got her out of Number 10 in July if that’s what they wanted to do; now, they’ll have to wait until the middle of next year if they don’t want to cause themselves problems. Having May go post-March 2019 and then allowing a new leader to bed in is a decent enough political narrative should you want to extend the current parliament as much as possible (and the Tories most definitely do). Getting rid of her now just makes the Conservative Party look even more of a mess. Particularly if Boris takes over as PM, which I very much doubt will happen now. His colleagues have figured out that he isn’t a serious politician and will always treat the whole thing like it’s a game of student politics.
As for Boris causing problems on there backbenches, he is already acting like a backbencher anyhow, saying whatever he likes. Given this was a woman who happy enough to sack George Osborne, I can’t see why she’s worried about what Boris will do (unless she’s learned from that experience and feels chastened by it, I suppose). Also, there is no collective cabinet responsibility in place at present – and there won’t be until she sacks Boris from it.
I get that May wants to keep her head down in order to stick around as long as she can. But she has to face up to the fact that in Boris she has someone who is not going to play ball on that front. Whatever the perceived risk of sacking him, if she keeps allowing Boris to say whatever he likes she might as well not be there. For now, the Conservative Party needs her, if only to avoid a leadership contest that would rip them apart. She should stamp her authority on the situation as much is available to her and sack Boris as soon as possible.