I’ve it set to check every hour and to notify me yet I don’t see anything new until I open the app.
It only worked for me only once. After that like you say.
Please file a bug, and here are some good guidelines for you to attach all
the necessary information to that bug:
https://wiki.mozilla.org/Gaia/Email/RequiredBugInfo
After you file the bug, you can set a ni? on asuth@mozilla.com, and he can
see what’s going on 
It seems that if the app has not been opened then the sync won’t work.
@mhenretty I have filed a bug. I will move it to the right component and do as requested.