How you setup Gmail in the "Apple" mail app is very critical.
Most people use the Add Account then select "Gmail". That in theory does work but it forces your phone to do a LOT of extra work (IE eats battery) for no benefit and is a pull email setup.
Instead setup the gmail account thru Microsoft Exchange. You get PUSH email for the GMail account and you can see everything with a few tweak instantly.
Now for the quick setup lesson:
1) Settings
2) Mail, Contacts, Calendars.
3) Add Account...
4) Microsoft Exchange
5) Fill in EMAIL, USERNAME, PASSWORD and DESCRIPTION ONLY
When you hit next, it will query the system and then present a new dialog
6) Server - Put in - m.google.com
7) Save - And that is the hard part done.
8) Go back to the list of accounts.
9) Fetch New Data
10) Push - Turn it on.
11) Advanced - Make sure you have the accounts set for PUSH that support it.
Now click on the account itself. This will allow you to chose "Mail Days to Sync" and "Mail folders to Push". Check off the folders you need notification on as well as how many days to keep on your phone at any given time and you are good to go.
Exit settings because you are done.