That I think is the fundamental problem. It's not unique to May, or even to the UK, either. You see this all the time. Politicians want to win the next election more than they want to do the right thing (or even the right thing according to their own views). But if you can't do what you think should be done, what's the point of having power?
There is no reason to believe MPs can "do the right thing". Their analysis skills are weak, they routinely say things that are factually false, they manipulate, they lie and their numeracy skills are nearly non-existent.
Some examples. Most of them can't even tell you what the probability of flipping two heads in a row is:
https://www.bbc.com/news/uk-19801666
The Shadow Home Secretary, i.e. the woman who is one election victory away from running the police, went on public radio and simply made numbers up off the top of her head for how much money would be spent on the police. Even worse the numbers were absurd, like costing only £300,000 pounds to hire 10,000 police officers:
https://www.independent.co.uk/news/uk/politics/diane-abbot-l...
It's clear that Theresa May and most MPs don't even understand the basics of negotiation, like "you must be willing to walk away".
Politicians should absolutely not be doing what they think the right thing is, they are wildly unqualified to decide that. Their job is to do what their voters ask them to do, as faithfully as possible, and nothing else. It's when politicians start to think they know better than their voters that power has corrupted them and the problems really start. That's the root of all dictatorships and the sorts of miseries that have throughout history killed millions of people.
There are lots of MPs who would want nothing more than to scrap Brexit or at least hold a second referendum. However, the situation is similar to what's happening with Trump and the Republican Party in the US: Politicians vote on party lines against their personal beliefs (or the desires of their constituents) simply so the party can hold on to power.
May and the Tories can't backpedal on Brexit because it would, at this point, be political suicide. It would significantly weaken the Conservative Party (the Tories) politically, and pave the way for a Labour government. May and her colleagues would prefer Brexit to losing their power. Of course, May says she sees it as her duty to fulfill the "will of the people" despite the fact that, according to insiders, she doesn't actually believe in Brexit.
What's remarkable is that the Conservative leadership has never been able swing the rhetoric around in their favour. A more cunning politican should have been able to turn David Cameron (who was responsible for setting Brexit in motion in the first place) into a scapegoat as well as point the finger at the Brexit faction for poisoning the well. There's a whole group of politicians, including Boris Johnson, that are now hated by the general public following the revelations about the Leave campaign.
What's also remarkable is how badly Labour has miscalculated the opportunity to gain a huge political momentum by becoming the anti-Brexit party. But its leader, Jeremy Corbyn, is an EU skeptic, and hasn't stepped up.