Every couple of months I encounter the same problem: GMail stops pushing mails to my iPhone. I just ran into that problem again last night.
Rebooting the iPhone, re-setting according options to „push“ and even deleting/re-adding the account(s) in question didn’t work.
What did work is:
Going to Settings -> Mail, Contacts, Calendars -> [Account Name] -> Mail Folders to push — and then selecting „[Gmail] All Mail“.
If you’re lucky this might work for you as well…
Keep in mind: when normal pushing starts working again, you will hear to „bings“ for each mail that arrives, one for „Inbox“ and one for „All Mail“. You can take that as your signal to unselect the „All Mail“ folder again, and then decide wether you’d like to revert the above changes.