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Cleaning the cache and restarting works only temporary for me. I didn't optimize for doze in battery settings apps that send me notification and that works now. When I optimize those apps problems again. I think Doze in Android Nougat is more aggressive then Doze in Android Marshmallow.
Yup, the same with Gmail for me. I usually leave my phone in the locker at the gym. When I get back to it, all other notifications are there (Facebook, etc) but only Gmail starts to update when I manually turn on the screen.
Don't have Yahoo. Using the F8332 Dual SIM, not sure what version. I've switched to Google Inbox though, and notifications are stable with this.
I have the same problems with Gmail, Outlook and other apps, such as Sofascore. The notifications arrive but a few hours late.
This is on a brand new XZ (F8331) running Android 7.1.1
For some reason on my new xperia xz the system had optimised all apps for battery consumption because I was having the same problem. Go to settings, battery then battery optimisation and reselect all apps that you don't want restricted in background and notifications should work.