Are you saying that if you look in Settings -> Battery -> History details (reached by touching the graph) that there are breaks in the Wi-Fi signal line (not accounted for by being out of Wi-Fi range)?Even if under the wifi settings you set the wifi never to sleep, it still sleeps.
The only time I notice that is when the phone is 'sleeping' (i.e. I haven't used it in some time and it's been untouched) - as soon as I pick it up and the screen wakes it suddenly shows all of these notifications that I've missed. Note that this is not limited to Gmail; all of the apps seem to do this.Anybody still facing this issue with Gmail Notifications popping in late on your devices?