Likely what happens is this [I just reconstructed your same problem here, so...]
If you close the KMix window, it just goes and docks in your panel. Doesn't quit. If you then close KMix in the panel, and restart it, it only comes up in the panel - doesn't show the window. When you then "start" it again, it realises it's already running and assumes you want to bring up the KMix window.
My guess? Settings -> Configure KMix -> uncheck "Dock in panel"
I'm running KDE 3.1 on this side, so I hope for your sake the option is there.
Hope this helps you out.
I'm using kde2.2 but "dock in panel" is unchecked.