A Difficult Case of "A transport-level error has occurred when receiving results from the server" SQL Server
I'm not sure what authentication method you are using, but I've seen issues when using Windows Authentication when the DC (Domain Controller) is being overwhelmed with requests you can see issues.  Usually it is a timeout issue though.

If you are using Windows Auth, try switching to SQL Auth to rule that out.  Sorry I tried to add a comment but it wouldnt let me b/c i'm new.