You'll get the same error if the server is restarted or if someone killed your SPID.
I always respect your words but the Error msg we recieve for the above situation is somewhat different. it is like this ..
Msg 233, Level 20, State 0, Line 0
A transport-level error has occurred when sending the request to the server. (provider: Shared Memory Provider, error: 0 - No process is on the other end of the pipe.)
yes, it is also a trasport layer error because the connection with the server has got disconnected but it is somewhat different.
Can you look on this link, without knowing much about the N/W configuration i will not be able to comment much because it does not seems to me an sql server specific issue because as you said it got randomly disconnected so pls check the below link out...