Android - Gmail app doesn't sync email at all when on Mobile Data

Ensure that on the device Settings | Data usage | Mobile | Mobile data is set to ON and that if Set mobile data limit is checked that you haven't reached that limit.

Found out the problem. Orange Wap was selected instead of Orange Internet in Settings > Access Point Names.

Just found this thread and it helped me solve the same issue (gmail not syncing on mobile data) on my Galaxy S3. Under settings/data usage/gmail I found that 'restrict background data' was ON. Just for gmail, not globally. Not sure when or how that got checked, but it may have been that way out of the box since my gmail has never synced on mobile data, even with a factory wipe.

Anyways, hope that helps someone else out there.