I haven't had problems like that for a while. When I did, it was a networking issue (Zaerc worked around, and a fix has now been integrated into later 0710 versions) in the way LMCE was using CIFS. Have you tried switching to SMBFS to see if that solves the problem.
Other options are, obviously don't forget real networking issues on your network - these may not be apparent due to automounting, etc in other areas, but very high volume copying could easily be disrupted. (and ripping to remote shares - which is another issue I have had unrelated to the CIFS issue, but seemingly no more since RC1/2)
Common ones would be NIC issues at both ends, drivers for them, the switch in the middle, or duplexing. Try connecting a cross over cable directly from source to destination bypassing the switch. Also try forcing full-duplex/100/1000 on both ends rather than auto-neg as different manufacturers have different interpretations of the auto-neg process. You may even have to sniff the traffic to see what happens when the com fails.