Might just be my American frame of reference, but May seems to be in a similar spot to where John Boehner was. She's in charge of a nominal majority but there's a hardline faction that won't back any deal that's acceptable to her negotiating partner (Obama's the EU in this). The obvious solution would be to make up for those votes by compromising with the opposition party, but she's refused to do that.
If she steps down and that's still the dynamic as they move on to the next set of talks, doesn't that just lead to the same type of dysfunction with someone else at the head?