Im sorry, but I am not understanding your question, so I will just post some feedback to help diagnose.
Starting from the left side of the Task Bar....."Quick Launch"-->is actually just a toolbar for shortcuts to frequently used programs, so you don't have to click "Start"/All Programs......
The "Notification Area" or "Tray" is where the clock is, and shows the active programs running,if desired, which I hate personally and I turn all of them off except the Internet Icon. They take up space, and if you want to display them, just click the "<" sign.
"Show Links" is also just a toolbar, and has nothing to do with the way Windows presents active programs, in fact, it is just a mirror of the "Links" option in your "Favorites" menu in Internet Explorer.
In between all that junk, is the actuall "Task Bar" where tabs for open windows run, and if you have chosen a program to minimize to the "Tray", then it will usually auto hide after a given time. That is a per program setting,found in Options, Properties, Preferences...etc
In my experience, I have noticed that the "Tray" has amnesia, I to have fought with icons. This is not a major concern to my knowledge, just a minor bug.
Sorry if you already know all this, but there are just so many variables involved, and the more information about the problem the better.