This is a very common problem.
Every person has a limited amount of space on the mail servers.
There is a soft and a hard limit. The soft limit is the quota, and the hard limit is called the limit. There are several ways for an account to go over the quota. If the customer uses Eudora to check their mail, then make sure that in the Eudora settings that the 'leave mail on server' option is unchecked. Another common cause is someone using pine or elm to check their mail and then saving attachments in their home directory.