SQL Server Connectivity Issues
OK, so odds are it isn't link that Up_One posted.

SQL Server does all it's work via schedulers.  Each scheduler is attached to a CPU core on the server.  Usually when I've seen that error it's because the CPUs are very busy and can't properly respond to the request in the time needed.

What's the CPU workload on the SQL Server look like when the problem happens?  How many users are running queries at that time?  How many CPU cores does the server have?

The fix is to reduce the CPU workload on the server.  Typically this is done by doing index tuning on the system which will reduce CPU workload.