Since late last year, there have been reports of Nexus devices running Android Marshmallow not getting Gmail notifications until the app was manually opened. Google has been investigating the issue for a while now and has finally come up with a fix that will be rolled out to users over the next week.
Gmail sync issues Stories February 10, 2016
Gmail sync issues Stories January 22, 2016
Gmail update fixes Hotmail sync issue, but not missing notifications on Nexus devices yet
Earlier this week, Gmail for Android version 5.10 shipped with a fix for a sync issue involving Hotmail accounts. However, Google is still working on a bug that prevents Nexus devices in particular from getting notified about incoming Gmail messages.