Want to add that I've also experienced the same thing a couple times with similar mods (Space Exploration). Symptoms and the fix are exactly the same as reported; auto trash continues to function, but the GUI config button stops working. /at_reset makes the GUI show and reinstalling auto trash restores functionality. Unlike OP, I have not set anything as a main network, but do use it to switch between profiles for being planetside or in space.
My best guess is it has something to do with how Space Exploration moves your character between different areas when you use spaceships/rockets. Were any new checks to the location/status of the player character added to auto trash in recent versions? I can't recall ever having this issue prior to the big auto trash GUI update, and I've been playing various versions of the Space Exploration mod long before then. It's also possible that Space Exploration may have changed something recently that makes auto trash sometimes lose track of you and think you shouldn't be able to access the GUI or something.
I'd provide a save but my game uses over a dozen random mods (one custom) and is over 250MB in size so uhh, it's not the most practical.