RoboCopy fails with "the specified network name is no longer available"

Robocopy is merely reporting what Windows has told it, that the remote end is no longer available, which can be a right pain to debug.

If you have antivirus software on the machines do a test run with that disabled. It's possible that the AV scanner isn't keeping up properly and causes things to hang while it tries to catch up. If that works you may need to disable the AV scanner on at least one end for the duration of the transfer. Also ensure that there is no firewall involved that might misinterpret the traffic and cause the the connection to be broken.

As a side note, that's a lot of traffic over such low speed NICs. You might consider adding a 1GB NIC to each machine, possibly connected by a crossover cable if you have no suitable switch ports available, and having that traffic routed through those NICs.