So far, magnets seem to be the answer. I don’t know how long super glue will last in this Southern heat and humidity, though.
Seriously…
Just write a note and leave it in your mailbox; don’t bother with calling the postmaster or “making a complaint.”
Just write a note on a Post-It that says “Hello Mail Carrier! I am having a problem with birds nesting in here; could you please close the door all the way? Thank you so much!” signed with your name. I’m a girl so I would add a smiley face.
I’ve written my mail carrier notes in the mail box, and the problem has always stopped there. Who could complain about a simple polite note? You’re not complaining; you’re politely requesting.