In Ubuntu (and Debian I believe, although I've not tested it) the slave zone files should be saved to the Bind working directory, ISPManager tries to save then to /etc/bind/.
The fix is simple, in ispmgr.conf change the value of path DomainSlaveZonesPath to .
Code:
path DomainSlaveZonesPath .
Rather than
Code:
path DomainSlaveZonesPath /etc/bind