If you think your Google Apps stored data are valuable enough, then don't waste time to search for a solution to save guard them- purchase full version Google Apps Backup software that take backup entire items of emails, contacts, calendars & documents from Google Apps account and migrate/convert/save Google Apps emails to PST or EML format as per user convenience. There can be multiple data stored in the Google Apps account which will go for a toss if any kind of error happened while accessing them- so expert advice is that get the backup of those data into any kind of offline email client like Outlook. PST or EML file format can be a safe platform to store entire data from the Google Apps account.
Make a reasonable investment and get the Google Apps Backup software installed in the Windows OS to take backup all those Google App email data into the safe destination of Outlook PST or EML.