David Cameron said about Theresa May that she was good at her job but you just couldn't reason with her so it was just easier to let her get on with it. But when there was a problem in the Home Office, it's interesting to note that it was Cameron that came out and did the PR on it, not May. I think that shows 2 things. One, maybe she didn't take advice when she was PM on how things looked, and 2, she lacked resonance with the public.
Both reasons why she didn't do well as PM.
As for sexism, that definitely plays a part. In the 1970s,and 80s Mrs T was definitely abused on a sexist fashion, she just didn't seem to give a shit. I think it was the 1987 election, Kinnock looked a shoe in. The Labour Party were doing a behind the scenes documentary they were so sure they were going to win. Then about 2 days before the election, labour did satirical party political broadcast aimed at wavering tory voters, criticising Thatcher in a sexist way, talking about handbags, bossiness, etc. Unfortunately for the men who made that PPB, Scarfe, Rushton et al, it seemed the voters didn't appreciate the blatent sexism couched as a bit if banter, and the LP documentary that was subsequently released said that they felt the pushback immediately from voters, and, of course, they lost the election.
I'm not sure how much has changed since the 1980s and I think Mrs M was also undermined because of being a woman, just these days they have to be a lot more underhand about it. But, mainly, she was unsuccessful at the general election and the Tory party are all about winning. If they think they'd win, they'd elect a chewing gum on a stick. Equally, if they display they can't win, they'll discover just how many knives can be stuck in their back at one time!