Here is another possible explanation.
After a while, the bent-over wires that serve as hinges for the lid loosen up. As a result, the lid may not be quite in line with the rest of the cage when you snap down the latch that holds the lid in place. The spindle is on the lid so when the lid is slightly out of alignment with the rest of the cage, the cage will not rotate perfectly parallel to the chaff tray. Some part of the cage will bump the tray. If the cage gets far enough out of alignment, it can actually lock up against the chaff tray. Burnt beans, big mess, been there, done that.
You can squeeze the hinges tighter with pliers, but just be sure the lid is centered over the end of the cage when you snap down the latch.