@morrow without logs this will be hard to track down. can you ask your administrator to open up a support case for this?
When you do not have a local MTA configured on the server with Zarafa installed, you need to run the Zarafa-dagent via Fetchmail. In fetchmail configuration file you should at the following option: mda "/usr/sbin/zarafa-dagent username"
See a full example fetchmail configuration below:
set postmaster user
mda "/usr/bin/zarafa-dagent john"
The fetchmail configuration should be made for every user individual.
See here for more information about Fetchmail.