It sounds like a similar problem to the one I am having . I just recently purchased my 2005 Crossfire Roadster , and oh boy have I found some issues . One of which I spent a ton of time researching , Something I would try is pulling the CPU re-soldering the joints and putting it back in this worked for me; temporarily . (But I think it may be because the CPU reset) .

Something else I would try is ; and I know it sounds cringe but hitting a bump with some speed, if your windows roll down , then the problem is for sure the same problem I am having ; the Head-bar convertible top sensor . The sensor is is what triggers the windows to move up and down when the top goes down . Apparently it isn't unheard of , and these sensors go out with some frequency .

My current problem is finding this part , I cannot find a place to purchase this sensor anywhere ! So If my help, helps you. Maybe you can link me to the Top Headbar Sensor .

Hope I could help a little , and I hope you solve the problem that you're having with your vehicle !