So here's my guess as to what's going on now, the why of it:

May is closing off all other avenues of escape (extension, repeal, referendum II) in the hopes that the prospect of default no-deal will frighten her opponents into reconsidering and accepting her deal, the one they rejected so decisively.

Meanwhile, her opponents are refusing to accept the same deal in the hopes that the prospect of default no-deal will frighten May into accepting some other avenue of escape, the ones she's been ruling out.

If nobody gives in, and I don't see why they would, they all go off the cliff together and take the country with them.

Same thing's going on in the US, by the way. Trump has boxed himself into a position where anything other than full funding for his wall would be a crushing defeat, so he won't accept any budget without it. Meanwhile the Congress absolutely won't fund it. So the shutdown continues.

Again, this could go on until the next election, or longer. It's not a Democrat v. Republican thing. The previously Republican Congress was equally uninterested in funding the wall, it's just that there were no political points for Trump in pressing the issue until the Democrats took office.

A previous case in US history that I've read about, featuring such a standoff, was the battle between President Garfield and Senator Conkling in 1881 over control of New York patronage. Both men quickly got to a position where for either of them to back down an inch would be a complete defeat. That impasse cracked with a surprising and completely out of the blue event on July 2.