Schedule report fails to email to all recipients when one has a full inbox

[Stevo]

Hi All,
When you email out reports (PDF, Excel output, etc.) in Cognos, from a job that might have a number of recipients, is it normal to get a failure in the emailing of those reports when just one of the recipient's inbox is full?  It seems that for some scheduled jobs we are running, no reports are received by any of the recipients when one of the people in the list has a full inbox.
I do not believe that this is normal Cognos behaviour but would like to know if anyone else has seen/solved this problem.  I'm inclined to believe that it is an issue with MS Exchange.
Regards.