According to one of the users affected by this, “I’ll send a test email to myself and the 6P never notifies me of the email, even after many hours. Contrarily, my Nexus 9 and old OnePlus One sync notify me just fine. I set up the Gmail settings the same say I have it on both of those devices and have made sure that sync is in fact on. It won’t sync without a manual refresh.”
So what can be done about this? Some have tried deleting their Google account from their phone and reading it, restarted, cleared the cache, and whatnot, but it seems that it has not worked. It has worked for some but it seems that this isn’t a universal fix as some users are still experiencing issues even after.
According to the responses on the thread, Google is aware of the problem so hopefully Nexus owners can expect a fix soon. That being said it does not seem that the problem is too widespread so if you’re not affected by it, don’t worry too much about it.