I think that the EU may have just shot her fox.
If France holds to the position they've just adopted - that they won't accede to the short delay unless she can provide evidence beforehand that she'll deliver a result - then she has a handful of days (maybe just three) to bribe and cajole a majority for her 'deal', or she's obliged to go cap-in-hand to the EU for the long delay. Which, of course, makes Remain more likely. Interesting times.
"the strategy is very obvious"
Watched her "speech". I would have laughed if I wasn't so worried about my pension. It was like Endora Stephens from Bewitched trying out hypnosis for the first time: "You're feeling sleepy, you're tired of Brexit, your eyes are closing, I'm on your side, you want my deal, MPs are to blame, you will hear only my voice..."
In any normal circumstances that speech would have been the setup for a resignation, not with May.
She really does not seem to either grasp or care (not sure which) that after a hard brexit and all the ensuing disasters, she will be the most reviled PM in history. Apologies to Neville, Maggie, and Tony.
You missed Cameron from that list. He reintroduced entitlement as a primary qualification for government, imposed a savage austerity on the UK that saw an unprecedented rise in rough-sleeping and food banks, and vastly accelerated the flow of wealth upwards to the richest. Then, scared of his party's right-wing and constantly overshadowed by his Bullingdon Club sibling, Boris Johnson, he called the referendum, made a pitiful half-arsed attempt to lead the Remain campaign, lost, and then fucked off as though it had nothing to do with him. The little shit has even suggested, recently, that he still has something to "offer" in government.
But yes, as Ant suggests, a resignation would be long overdue for anybody with any sense of shame. Unfortunately it's beginning to look as though she's determined to persist in order to ensure that the UK leaves the EU without a deal i.e. to carry out her threat. After meeting her yesterday, Anna Soubry said that she seemed delusional "quite seriously".
She certainly looks mentally unfit, by some combination of (no doubt prescription) drug abuse and exhaustion.