Corbyn has been lauded for his performance but all that's happened is that he wasn't stuffed as expected, but instead had an honorable defeat. But it's still a defeat and by a fair margin.
However I think he should stay on because if the Conservative /DUP love -in falls apart this year then they'll be another election and the Corbyn bounce might still propel Labour into power.
Longer the coalition lasts less likely it is for Corbyn to keep the wave of enthusiasm for him that he has now.
So if I was advising Labour I'd get rid of him if there's no election by middle of next year.
The Conservatives will NEVER let May lead the party again into an election, so she is toast sooner or later.
As for the actual coalition this could be problematic for the Northern Ireland peace process. The British Government is supposed to be neutral in discussions between Unionists and Nationalists, but that can't possibly work now with the DUP propping up the Government.