I hired a convertible a couple of years ago to drive around California/Las Vegas/Route 66 etc. On anything but a bone dry, billiard table smooth road the ride was awful. On some of the older, more worn sections of Route 66 the car became quite uncontrollable and on a wet road getting the power (or rather the lack of power) down was quite a tricky feat.
All this in a new car having covered less than 3000 miles. Quite a disappointing car really.
Last year we had a brand new convertible Camaro, now that WAS rather nice!!