Owners of Nexus devices have been experiencing some syncing issues with their Inbox or Gmail accounts.
According to posts on the Google Nexus Help Forum and the AOSP Issue tracker, it seems that there are quite a few users who are afflicted by the issue. It appears to be a known issue that the Android team is supposedly working on.
Essentially, what is going on is that notifications for Gmail, Inbox and a few other apps are not coming in when they should be, Ubergizmo reported. They are either coming in much later, or not at all. In addition, there is an issue with Google Now and less definable errors.
The issue tracker entry has been starred by 140 people in the forum thread, indicating a fairly widespread problem, though it is not universal. Various esoteric solutions like wiping the cache, resetting Google accounts, or flashing back to earlier Android builds and then applying the update do not seem to resolve the issue, and they are affecting a wide variety of Nexus phones and tablets.
A few users in the AOSP issue tracker thread have noted that this may be due to the Doze feature included in Android 6.0. Some users have noted that the issue has been solved by turning off Doze. But it has only worked for some and not everyone that has been having the issue.
Google representatives have replied to both threads, so the Android team is almost certainly aware of the problem at this point, according to Android Police. Various users have posited that the issue stems from Android 6.0's power-saving Doze feature.