Android 6.0 Marshmallow for all its wonderful new additions to the operating system like Doze mode and the granular permissions, still has a few quirks that are causing problems for users. The issue at hand this time around focuses on the syncing problems that users have been having with Gmail. The problem was reported on back at the beginning of January, although users had been having problems with it since before then, and at the time, Google had stated they were aware of the problem and were working on a fix for the issue. The good and bad news is that a new version of Gmail has been pushed out as of a couple of days ago and it's fixing the sync issues for anyone who has connected their Hotmail account through the Gmail app.
While Gmail version 5.10 fixes the sync with Hotmail accounts in Gmail, what it doesn't fix is the sync issues for any other accounts, which was initially the problem in the first place as people were experiencing sync issues and a delay in the notifications for their actual Gmail accounts as well as Inbox on Nexus devices that had Android 6.0 installed. It's worth mentioning that the Hotmail account sync fix comes along with the update to Gmail 5.10, but that version of the app is rolling out slowly to users according to Google so there could still be a bit of a wait for the app to make it to users officially. If you aren't one for waiting, you can download the Gmail 5.10 apk from the link below and install immediately.
For users who are waiting on the fix for the Gmail sync and notification delays for Google accounts, as stated the fix to correct the problem is still being worked on although hopefully it won't be much longer. Plenty of discussion on the matter is continuing to take place over on the Nexus Help Forums, with a possible short term fix stated by some users being to disable Doze mode, although there is no guarantee this will work for every user having these problems, and as you would have to disable something to fix something else, this isn't a correction users should be expecting as a complete fix.