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Speculating. One possible scenario.
Maybe Flynn was forced to resign because he did nothing more than lie to the vice president; the president knew about it and planned to simply let it go without saying anything to Pence. From Trump's business experience, its not uncommon for staff to lie\BS to each other, so its no big deal as long as they are not deceptive with him.
Next, insider info is leaked to the media and Pence figures out he has been lied to by Flynn. He confronts Trump asking him what's going on, Trump throws Pence a sale pitch of BS, but Pence doesn't buy any of it. Pence informs the President that he can't work with Flynn going forward and let the president know he'll resign with 24 hours if Flynn remains with Administration.
Bottom line, Trump would prefer to keep Flynn and let go Pence, Trump but is smart enough to understand the impact it would have if the vice President resigned after 30 days, plus making public everything that happened, and how the administration was keeping him out of the loop.
Flynn, the loyal soldier, takes the bullet... And who knows, may asked to come back later in a different position that does not have any connection with the VP.