I think these two might have been taking themselves just a little too seriously. I actually think I can relate. I tend to have a mission-driven personality myself, and I know how hard it is to accept when all objective facts tell you the mission can't be accomplished.
I'll find another way! Some way! There has to be a way!
Strzok and Page seem to have been so invested in the stop-Trump-at-all-costs mission that even after he won - the very definition of failing to stop him - they weren't quite ready to process it was time to move on. They'd already compromised the integrity of the FBI by covering up Hillary's claims while trumping up charges against Trump, so hey. In for a dime, in for a dollar, right?