I'm investigating a different track as well, I was always wondering about the SAN track, since the SQL Agent error refers to TCP, i.e issues in the TCP stack, and the parameters mentioned in this thread also refes to tcp/ip.
Our test have been to disable the Arcserve open file agent, this is a kernel driver, that loads deep down in the tcp/ip stack (ofant.sys). Stopping the windows service is not enough since the driver stays loaded, so we went for an uninstall. Only two weeks after uninstall but have not seen any issues yet.
I mention Arcserve, but I guess all backup poducts have similar agents for backing up open files.
More news after some time running in this configuration...