I'm having the same issue but also a fair amount of flash. The worst was a giant piece inside the name groove of the plastic piece. I also was using a piece from the game to push them in further...like an idiot. Got the cardboard shredded on one side.
I sent an email to the store I bought it from hoping for a replacement base but we shall see.
You need to contact FFG for a replacement part. Odds are good they'll drop it in the mail before you get your confirmation they received your request. They have a webpage dedicated to replacement parts.