It should. Try removing the account and adding it again. I have to do this with Yahoo! from time to time to get the push going again. Not sure if its been iOS or something else but this has worked most of the time.
This happened to me when I upgraded to the iPhone 5s I believe.
Gmail no longer supports push in the iOS native mail app. If you had a device that was using push before this new policy went into place you are ok. As soon as you set up that mail account on a new apple device you would not have the push option anymore.