Like any car with features like the Soleil if the roof is neglected they can fail and cost a fair bit to replace. 899cc won't blow any socks off, 90's Polzka Fiat build quality (or lack there of), rust and they're mostly pensioner/student cars so have either never seen more than 40mph or have regularly been hammered along Halfords car parks at night. From the list of things wrong with the car I've bought and modifications I'd say the latter is most likely the case.
Hopefully the car is at the tipping point where it would be scrap yard bound if it wasn't for some idiot buying it to restore.