Never had this problem.  But a few thoughts on yours..

You might check the wheel balance, if the wheel was out of balance, the eccentric forces will loosen the cap's grip.  Check the tire tread, if you see cupping of the tread, it's definitely out of balance and is "bouncing" on the road. 

Also, you might make sure the wire grips are tight and correctly gripping the lug nut.

There was a redesign on these. An '01 should be old style, so the replacements should work much better.

RTSmith