I believe that Trump will not recover from his "pu**y" assault video I think he will lose and lose big in November. Of course, he has a business that he can go back to.
But, Mike Pence is still in politics, and politics can be unforgiving; especially if Pence has any thoughts of running for president in 2020. By not leaving the Trump ticket, he will be seen as condoning that behavior, and no amount of "forgiveness" is going to help his political career going forward. Forevermore, he's now tainted by Donald Trump. Just as Billy Bush's career will never be the same.
Pence emerges in NC with praise, ‘forgiveness’ for Trump: https://www.washingtonpost.com/politics/pence-emerges-in-nc-with-praise-forgiveness-for-trump/2016/10/10/0bca144c-8f34-11e6-bc00-1a9756d4111b_story.html
Pence: I never considered leaving Trump ticket: http://www.cnn.com/2016/10/10/politics/mike-pence-donald-trump/
Mike Pence’s Fellow Parishioners Are Furious at Donald Trump: The parishioners I spoke to are angry with Trump for exposing the Pence family to such shame: http://www.thedailybeast.com/articles/2016/10/10/mike-pence-s-fellow-parishioners-are-furious-at-donald-trump.html
'Devastated' Billy Bush 'Can't Recover' from Leaked Donald Trump Tape: http://people.com/tv/devastated-billy-bush-cant-recover-from-leaked-donald-trump-tape/
Billy Bush is reportedly leaving NBC after vulgar Donald Trump tape leak: http://www.businessinsider.com/billy-bush-is-leaving-nbc-donald-trump-tape-2016-10