I would check to see if it happens if you swap out the network card in the machine (or machines) that is crashing with a different (and hopefully better) one. There are a LOT of crappy network cards (both wireless and wired) out there that can cause problems like this.
I've had trouble in the past with sustained network activity (and experienced problems similar to yours) with Netgear and Linksys cards for example. Once I switched to a high quality 3Com card (I LOVE my 3Com cards) though, the issue went away (and my transfer rates and CPU usage rates fixed themselves too). You also mentioned a Linksys router. You could be killing the router with sustained traffic (do you have to reboot the router ever after this happens to get back online)? Check out
www.broadbandreports.com for more info on your router and to see if firmware updates have helped others (sometimes the updates make the problems with those things worse). If it turns out to be router related, I'd check into smoothwall or monowall (google search them) before I buy a new one. My smoothie was the other major way I solved my network problems.
A good way to see if it's a general network problem (rather than a software issue or a problem with the USB drive) is to try to slam the network/card with traffic. An easy way to do this would be to download the bittorrent of a fedora linux release (
fedora.redhat.com) The bittorrents of those get going crazy fast on my cable modem (and were sufficent to lock up both my Linksys network cards and my old Netgear router within an hour when I was testing).
One other thing to test would be to see if the USB drive is crapping out on you. Lots of manufacturers sell USB2.0 drives that really can't sustain USB2.0 speeds (check out reports at Tom's Hardware, HardOCP, Anandtech, etc). Try doing the same size of import from an internal drive on the server system and see if it is any different.
Sorry about the book-length reply. I've just been down that road myself though. Hope this helps!