I use Google Keep on my Android phone. The reminder notifications didn't pop up anymore. I checked all the settings on the Notifications Manager on my phone, all was well, notifications were switched on for Keep.
As a test I opened Keep in my browser on a desktop PC (browse to https://keep.google.com). I set a reminder. At the time it was due it popped up on my PC and also on my phone! Since this time the reminders have been working on my phone.
I do not understand why and I am keeping my eye on this. It's September 2016 at the time of writing, perhaps there will be a fix in the future, let's hope so. If you have had this issue and you've solved it a different way, please comment here.