Ever since, whatever update to the native gmail app, added the"priority inbox", I have not received notifications. In fact, no mail shows up in my inbox at all (neither priority our regular inboxes). I have to open the all mail label and then my inbox (and priority inbox) populates and my phone registers a notification. This is extremely annoying since I used to be able to know exactly when I received a new message, and now I have to check repeatedly throughout the day. I've tried some different settings in the app and on the web, but I just wish I could completely get rid of the priority inbox in the app altogether as I really don't need it.