Check all the screws, especially the ones on the bottom, are all nice and tight. If they are, then the problem is that the hole the 'pin' the whole seat pivots on has worn, and there is no easy way to fix it.
Best thing to do is to find a replacement base. Unscrew your actual chair and bolt it onto the new base. The trick is finding one with the same hole positions.
DB
February 2009