I have Internet Explorer 6 installed and the Google toolbar addon. The only problem is that the Google toolbar can't seem to remember the position that I put it in sometimes and keeps changing its position by itself.
It's a bug in the toolbar.
I had that problem a few months ago and I submitted a bug to them. I got a reply of "known issue". They updated to a new version in December. I reinstalled with the new version and it now remains in place, but I still have problems "hiding" part of it. It stays on the line I put it on, but it "slides" over to show the whole thing instead of just the search/relevance portion.
Try to reinstall it and see if it'll stay put. If that doesn't work, I suspect it's still buggy.