I have the same issue. After turning in the requisition quests, they restart or pop up again as if I never turned them in. This happened to me on the quest where the woman asks for herbs in the Hinterlands and the dwarven puzzle box requisition quest. It's really annoying.
Edit: Perhaps these quests are supposed to be repeatable? Some repeat (like above) while other requisition quests do not, and this leads me to believe that it is a bug. The dwarven puzzle box is a repeat, but I cannot repeat the first one - Requisition for Weapons.