Mike Hays looks at a trace flag that can help you troubleshoot why client connections drop:
About once a month, I get support ticket regarding SQL Server dropping an application’s or user’s connection. The problem is SQL Server does not just randomly drop a connection and continue to work normally. Some force outside the control of SQL Server breaks the connection. By default, SQL Server does not record when this event occurs.
In my history of working with SQL Server, only in extreme situations have I ever seen SQL Server drop its connections. The most common example is when SQL Server is in the process of shutting down.
Click through for the trace flag and details.