It's probably normal convert flex. I've heard more than one person say that if you stick your fingure between the door and the quarter...then drive the car around a corner...your figure will get crushed. Seems like frame connectors are the fix. I wouldn't want to add them to a stock restored car though.
I've heard of people cutting open the rocker panels from underneith...then adding thick steel, the entire length of the rocker. The factory added a beam in there but it wasn't enough. Frame connectors would work better but for a restored car, something hidden would be a better choise I would think.