At the beginning of the play, Blanche tells Stella that the reason she isn't teaching is because she took a leave of absence due to stress - this was in early May. Obviously in the months June, July and August she wouldn't be teaching anyway due to summer vacation. Yet by scene 7, it's 14th September, Blanche's birthday, and she still hasn't returned to teaching. Obviously this is because in reality she had been fired, but surely by this point Stella should have been just a little bit suspicious? Any leave of absence that Blanche could hypothetically have been granted would certainly not have extended into the next academic year, yet Stella is happy to keep her without asking questions. Then again, it's been suggested that Stella doesn't really care about anything except sex with Stanley...
It's also possible that Stella knows that something's up, but just chooses to humour Blanche.
She seemed pretty shocked when she found out Blanche had been fired (along with the other stuff).
On that front, how is it that Blanche has an affair with one of her students, and yet the only consequence is that she's been fired? Doesn't that sort of thing warrant a jail sentence?
I'm pretty sure that as the student was 17 and the age of consent was 16 then, although it would have been seen as inapropriate there was nothing illegal about the affair.