1. The K-2 system does not stay open for me long enough to do my work. I need it open for hours, not minutes.

2. Because the K-2 demands password re-entry after 15 – 20 minutes, it puts up a password dialog box that does not accept any of my passwords

3. Because the dialog box cannot be cleared, to allow me to close the K-2 and re-boot, my complete system gets locked down.

It seems like the logon dialog you are referring to is a Windows login which indicates Kerberos issue. 

Does it pop up only when you access specific process' form, which might be accessing other servers?    Or is it even occuring if you are just running Workspace search and reporting?
 

That looks like a Kerberos issue since you do not use that login dialog to first sign into Workspace (it seems you are using AD).

When you get that, use Cancel button and check for Event Log to see if it mentions anything about Kerberos.   

Also is the process with the issue is hosted from a different server that K2 Workspace is running on?
 

sorry..we are using the same dialog box at the time of first login into the workspace.

yes..k2 workspace is running and hosted from other server