Exceeding Mailbox size limits

Our network uses Exchange 5.5 SP4 and Outlook. Many users are set up as receive-only. These users receive the “Your mailbox has exceeded one or more size limits set by your administrator…” message daily. I know this will occur when a user with this restriction tries to send E-mail, but this is occurring on accounts with totally clean boxes w/o having attempted a send. Any ideas to keep this from occurring every morning or is it a necessary evil?
Tanks, mon