I have spoken with tech support and have read every possible thread on how to correct the problem. I should add that I do receive notifications when I am on WiFi. Is it time for a replacement phone?
Welcome to Android Central! Have you already checked Settings>Data Usage to make sure Restrict Background Data isn't turned on (either universally, or specifically for Gmail)?
After 3 days or more of a not receiving Gmail push notifications and talking to different Tech Supports, I am now getting my notifications. Fingers are crossed.