SQL disconnect my user automatically time to time

My friends , I found an unusual problem with my software in last days , About two weeks before one of our applications which has been written with Borland Delphi 7 and uses ADO connection for connecting to Microsoft SQL Server 2005/2008 as Database Server stopped working fine .

In fact after each client starts the software and connects to the SQL Server database successfully Everything is going fine until the user stop working for a few seconds/minutes , Then when S/He come back to work an error message appears : Login failed for user ….. and So the user have to start the Application again until S/He could continue working .

We checked for Orphan SQL Server's users but we found nothing and even We checked the SQL Profiler but again found nothing useful .

The result of our tests is as following table :

ease Help us and If you have any advice for our problem it would be very appreciated .

Are you sure it is SQL Server dropping the connection or the software having a timed connection?

In fact it's not clear to me . I am searching for find out what really happens ?