A transport-level error has occurred when sending the request to the server. (provider: TCP Provider, error: 0 – An existing connection was forcibly closed by the remote host.)

msdn seems to have a reasonable description of the problem here.  However my SQL Server log does not contain any entries for the time of the failure.

The last message in the latest SQL ErrorLog file is at 04:29:58.48

My application reports the connection status as open at 05:21:37.781

The failure occurs at 05:21:37.875 – less than 0.1 seconds later!

There are no messages in the eventlog in this time period.