Stuck, how did missions/gathering make your crew stuck? Missions only takes your game time (but in real time they return instanly). The difference is that they have lesser happiness, and lesser compliance (They tend to not comply especially if they had low happiness and compliance) which which can be looked through their stats in GI/GU tab?
Are they actually missing from your ship?
I think also that crew members are unspammable (to do repeated missions) as the story is not finish yet because you need to make connections with them first so they would comply if they were assigned. (If you spam them abusively, they will not comply later on the game).