It looks like spamming has been happening from your server. Their remote mail server must have some sort of a mechanism which reject mails if found to exceed a particular quota. Your server needs to be checked for spamming..
The saver has very few accounts, and all accounts on this server are companies in my city, all are known customers and not online created accounts, I do monitor the message queue and statistics to see if anybody is sending SPAM, maybe that server blocked a range of IP's ??? or it could block only an IP and my server IP is blocked.
here is a short statistic of Top 50 local senders by volume
(Exim statistics from 2009-10-18 04:02:14 to 2009-10-21 19:08:36)
Messages Bytes Average Local sender
3975 313MB 81KB trxxxxxx // this is a local newspaper, all the messages are sent as a newsletter, NO SPAM, al recipients did subscribed to this newspaper
3112 260MB 86KB mailnull // ?????????????
1045 24MB 24KB design // this is one of mine domains, sending emails to another email I have (on another dedicated server) with some statistics
564 756KB 1372 root
7 36KB 5266 hhxxxxxx // client
23 30KB 1335 zaxxxx // client
4 15KB 3840 anxxxx // client
3 4320 1440 my3xxxxx
1 1501 1501 psxxxxxx
1 599 599 prxxxxxx
1 439 439 paxxxxxx