How to recover emails backed up in iCloud
This issue is most likely something to do with Gmail and it's syncing. Check Gmail.com to see if your mail is still there. 

If it is, try deleting your Gmail account from your iPad (Tap Settings > Mail, Contacts, Calendars > (your Gmail account) and press "Delete Account". Then add the account back by tapping Settings > Mail, Contacts, Calendars > New Account. Select Gmail and input your credentials. This should bring back your mail.

If you need to restore from an iCloud backup because the mail on your phone was archived locally and not synced to Gmail, restore from an iCloud backup as detailed in Apple's Support article:


Erase your iPad by tapping Settings > General > Reset All Content and Settings
After your iPad has been erased and your device has presented the greeting screen, follow the steps. Join a Wifi network, and follow the next steps. 
Tap "Restore from iCloud Backup". Sign into iCloud and choose the backup you want to restore to your device.
Continue to follow the steps until you have restored your iPad and your locally archived mail should be where it was put.