Things I've tried:
Clearing Gmail cache
Clearing Gmail app data + cache
Forcing a resync in Settings > accounts
This is what it looks like, you can see here 1 minute before the screenshot I forced a resync of my Google account, everything updates fine except for Gmail which is stuck on 2014-01-20.
After clearing app data + cache, Gmail is stuck on this screen:
The only way to workaround the issue is to remove my entire Google account and set it back up again on the device. This is not ideal, and the issue comes back at some point again.