Emails hitting size limit

Emails hitting size limit

We have Zoho CRM set up so that our Google Apps for Work mail is drawn into Zoho CRM via IMAP. There is size limit per mail account (5GB I think). We've had cases where users hit that limit and mail stops transferring into Zoho.

Since the mail function is pretty much a background function, not something where people regularly visit the Emails tab, it's easy to not realize that mail has stopped functioning.

Is there some central administrative way to monitor this and to delete old emails for users? Or, even better, to have older emails automatically deleted when the size limit is reached?

Thanks.