Could it be possible that you didn't actually purchase any belt (perhaps it was another gear piece instead) and the roll from the dungeon went to someone else?

I would suggest doing a test. When you purchase an item or gear it should say in the chat that it was placed in the player's Inventory or Armoury Chest. If you were to obtain some gear (the ARR starting cities like Limsa are cheap places to do this), see then what is recorded in the chat on purchase and also confirm if it actually gets placed there or not.

Obviously if there is still issues after testing that then could be a bug that probably needs to be reported.