You can look at car reviews for this model on the Edmunds.com web site. If the '06 model had a real issue it is likely later models were fitted with more frame and structural reinforcement to reduce body flex.
All convertibles need frame reinforcement over the standard hardtop of the same models. Some of the body integrity is lost when the hard top is replaced with a convertible top. Some manufacturers do a better job than others. The Chrysler Sebring convertibles were about he worst in recent history.