When the quota limit is about to be exceeded, you send a message to the customer before suspend the service.
It's the second time my company's services are suspended because our automatic backup ocupied more than our disk space.
I think that if the backup it's going to exceed the available space, it's better not to let the archive to be created and send a warning to the customer. Now instead, the service is suspended and the customer spends a whole day (or two) without email or webpage.

There is threshold for quota limit at which customer is notified. If the threshold is set empty or too high, or too low, then notification might not be seen in time.
Backup files have “rotation” option, so that only fixed number of backup files is stored. It is not quite possible to precisely calculate backup size in advance unfortunately.