Something else must have happened to cause that JC. Minor faction rep does not decay. Superpower rep does, down to 75% (Friendly), but superpower rep means nothing really. Minor faction rep doesn't decay due to inactivity, but actions taken by the player can cause it to drop. It's a reason to not bounty hunt in your home system for example.

And only faction rep affects the missions you are offered. Superpower rep does not. So there must be a different reason if the mission quality drop you saw was due to lowered minor faction rep.

I'm also based at a station with a mix of Fed and Imp factions, and I specifically sought it out for that reason.