The challenge with a convertible automobile is that not only is the top no longer "integral" to the structure (structurally, the top is "missing entirely"), but you have additional "flex points" on each side - where the doors are. You can't just reinforce the corners. There has to be additional floor reinforcements extending beyond both ends of the door openings.

Think of it this way:
Take an empty Cool Whip container, remove the top, duct tape a tennis ball to the middle of the bottom of the bowl and make four 2" cuts down the sides of the bowl with a pair of scissors (like cutting a pie into quarters) and then replace the top, putting four small pieces of duct tape holding the "sides" (areas of the bowl between the cuts) to the lid. This will simulate the rigidity of a coupe or sedan. Now roll it down the stairs. Watch the shape of the bowl. The bowl basically retains it's shape / structural integrity, flexing a bit, but not much. The structure inherantly returns to it's original shape as it absorbs impacts from the steps.

Now remove the tape and remove the lid from the container. This will simulate the rigidity (or lack thereof) of a convertible. Now roll the bowl (with the cuts and the tennis ball taped to the middle of the bottom) down the stairs and watch as the bowl flexes, shakes and changes direction more drastically than when the until was sealed.
The best way to reinforce the structure now is to tape popsicle sticks on the bottom / underside of the bowl spanning the cuts (that simulate the doors). While this helps the rigidity and reduces the propensity of the bowl to twist/wring, the tennis ball is still exposed and prone to ejection as a result of the forces on the bowl as it rolls down the stairs.

That's the best way I can simulate the differences between a coupe or sedan, and a convertible - and how they have to add weight in reinforcing to the frame/body to minimize the flexing that occurs in a convertible during a crash/rollover.
Hope that helps.