My passenger door was doing the same thing. If I pushed down on the window when the door was open it would drop the normal distance so you could close it without the window hanging up on the convertible top.
I found that with the window rolled 1/2 way down I could pull it up and down and make it move about 3/4 of an inch.
The cable system on the window regulator seemed to be stretched out, so I was able to at least temporarily fix mine by taking some of the slack out of the cable. Since there are no cable adjusters, I made one from a zip tie wire ties. See the pictures below. This fix allows the window to drop enough to clear the top and I'm going to look at adding a bicycle brake line adjuster to the system so that I can dial it in better.
Thank god the door panel comes off very easily, with only about 4 screws and some clips holding it on.
Instructions to remove the door panel can be found here:
http://www.bombaydigital.com/boxster/projects/window/
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