Can you remove the chain missing link too often? I became  pretty obsessed with my MTB maintenance. After every trip, I completely remove the chain and wash it. 
I am wondering if you can damage the missing (and weakest) link of the bike by doing that this often. 
Thanks.
Yes.  

Most sorts of reusable link generally have a "snap in" position that the link pops into when you pull on the chain.  Between normal chain tension and design, the link should stay in that position.  However, with repeated use, you can wear the portion of the link that is tight enough to keep the link in the running/together position.  This means the link may become easier to get off, but will also be susceptible to coming uncoupled when the chain has less tension on it.  

Your individual mileage on a quick link may vary, but generally they are much less expensive than a whole new chain and the reduced cost (to you) by keeping your drivetrain clean will likely be worth it.