Requested mail action aborted: exceeded storage allocation Error 552

Can anyone help me with this very difficult problem.   My department has a newsletter which is created through an interactive web page hosted by a company called Aristotle.  We upload picutres to their site and fill in text.  When we send out this newsletter it goes to outside email addresses - it isn't delivered to any of our emails in our domain.  We have a Barracuda and Exchange Server 6.5.7638.1.  There is no quarantine message coming through to recipients and I can find nothing in Exchange Server or Barracuda.  Looking at it from our end there doesn't seem to be anything even trying to come through.  But the error message below says "exceeded storage allocation."   I archived all the folders in my email account just to exclude this as a possibility but Aristotle's server still shows the same message.  
Current delivery status after 1 delivery attempts is:

Tue, 01 May 2007 14:51:05
- Email message received.

Tue, 01 May 2007 14:51:07
- The ID number of this incoming mail message is: 2078554

Tue, 01 May 2007 14:51:07
- This list posting is addressed to mailing list: 'department name' and subset: 'testsend'

Tue, 01 May 2007 14:51:07
- Created outgoing email job

Tue, 01 May 2007 14:51:08
- Preparing to deliver outgoing email message.

Tue, 01 May 2007 14:51:14
- Successfully sent to 6 out of 8 remaining recipients (75%) in
  6 seconds.

  Delivery statistics:
    * 6 successful recipients (75%)
    * 2 undeliverable recipients (25%)

Tue, 01 May 2007 14:51:14
- Next retry scheduled for: Tuesday, May 01 at 03:51 PM (in 1 hours)

---------------------------------------------------------------------
Detailed delivery report for each undeliverable member:

--> Sending email to: user@departmentname.org
<-- DNS lookup succeeded, found 1 acceptable mail servers for arkansasheritage.org
--> Attempting to connect to: mail.departmentname.org (170.94.19.5 25)
<-- Connected to: mail.departmentname.org (170.94.19.5 25)
<-- 220 SMTP service ready
--> HELO lyris.aristotle.net
<-- 250 Requested mail action okay, completed
--> MAIL FROM:<bounce-department name-11163044@lyrissql.aristotle.net>
<-- 250 Requested mail action okay, completed
--> RCPT TO:<user@departmentname.org>
<-- 250 Requested mail action okay, completed
--> DATA
<-- 354 Start mail input; end with <CRLF>.<CRLF>
--> (message body)
--> [sent entire message body]
<-- 552 Requested mail action aborted: exceeded storage allocation
--> QUIT
Start Free Trial