Hi,
Those one-hour tokens are for a different authentication type than we're using (the unattended type). The sites I'm backing up on Google Drive have never needed to be refreshed.
"Backup Now" is actually the same internally as the other scheduled (daily, weekly, etc.) backups - it just schedules for 5 seconds into the future (and doesn't repeat).
The only time that UD interacts with google.com regarding changing OAuth tokens is when you click the authenticate link. The only thing that happens at any other time (when backing up, downloading or deleting) is that it hands over the previously-gained token and hopes it works. But it can't try to replace the token, because the authentication method being used to gain a token requires a user to be present and to explicitly click on buttons on a page delivered from google.com.
So, I think something happened that caused your tokens to be expired at Google's end. But, I'm not sufficiently knowledgeable about Google's OAuth system to suggest what that could be, as I've not seen this before.
Only one thing: Google did change which permissions were required to download a backup in April 2013. If your tokens were from before April 2013, then that is probably the cause. There's a message about this locked on the top of our forum here: http://wordpress.org/support/plugin/updraftplus
David