We get similar error messages at random during the day. We're currently troubleshooting, but our best guess right now is network error. Also, we've gotten that error when we had a bad HBA card on the SAN.

It's time to involve your network & server teams. Have them put a sniffer on the server to see how packages are going in and out. Also, have them check the NICs, HBAs and cable connections to your box. But you might have to define a time frame for the sniffer, so log what times of the day you're getting this error and what jobs / queries are running when it happens.

Oh, and don't forget to check your SQL Server Surface Area Configuration to make sure you have remote logins enabled.