No email push notifications

I've been having the same problem. And it's not confined to the Gmail app. I also have the problem with the Yahoo mail app (which I'm forced to use because of a problem using a Yahoo (now Aabco) small business email account with Gmail). Despite both set to receive push email notifications, Gmail and Yahoo will frequently not show email until I open up the apps. To make things even more bizarre, I also have my work email app and Outlook.com set to receive push notification mail, and they work fine. Battery saver is off. There's a discussion on this in the Pixel XL community on Google but it goes nowhere . . . .
 
If you go to settings, notifications, and check notifications for Gmail - maybe it's turned off? Also check the ringtone, maybe it's set to silent or something... Just brainstorming some issues that could possibly be causing it
 
If you go to settings, notifications, and check notifications for Gmail - maybe it's turned off? Also check the ringtone, maybe it's set to silent or something... Just brainstorming some issues that could possibly be causing it

I've checked all of the obvious things. My Gmail account itself seems fine most of the time; other accounts in the Gmail app either don't play well at all or get delayed notiifcations (much more than the 15 minute default for non-push). Yahoo Mail -- forget it. For the time being, I've put all of my accounts except Gmail in the Outlook app. Seems to be working.