SQL Server Problem When Change Windows Admin Password

I need to change the Admin password on a Windows 2008R2 server. There is a software package running in SQL server that has its own account name and password for SQL server (which is using Windows authentication).  When I change the Windows Admin user password the software reports an error connecting to the db.  I'm not clear on why this happens since Windows authentication is being used and I thought this shouldn't affect the software package.  (I am admittedly not very knowledgeable about managing SQL server.)

How can I change the Windows password without causing a problem for the 3rd party database program.

Thank you.