Thanks for the question. The following article may provide a resolution to the symptoms you described:
- If the account is removed and added again to the device, this error appears: "Could not connect using SSL. Would you like to try setting up the account without SSL?" Saying yes to this message repeatedly will result in a message saying "Cannot Get Mail. The connection to the server 'imap.gmail.com' failed."
2. If you have other email accounts on the device, check if those accounts can send and receive email.
3. If the issue is isolated only to the affected Gmail account, visit this website: https://www.google.com/accounts/DisplayUnlockCaptcha.
Complete the form to unlock the account.
4. Once the account has been unlocked, check that the issue is resolved on the iPhone or iPod touch. If not, remove the affected Gmail account from the device and add it to the device again: Settings > Mail, Contacts and Calendars > Add Account > Gmail.