Is it just running every possible quest. Or is it first viewing the page with Quests for the day?
1 day I tried to get ahead of my quest log when I first logged on and so I did the usual ones like feed a pet, customize a pet, etc. Then when I went to the page they said I hadn't done it yet either.
So maybe start on the quest page first? If you already are then I'm not sure what would be causing your issue. Hopefully someone else can help!