When I got my 124 the only problem was the headlining was sagging and partially obscuring the rear window. I bought the car in Salt Lake City which does get quite cold in the Winter. It had been used as a demonstrator and it could well be that the lid had been exercised in cold weather. There's a plastic strip on the headlining that fits into a channel behind the seats and it must have popped out but had not been correctly re-installed. It's really tricky to do it properly but I eventually figured it out.Here's another. "Do not raise or lower the convertible top when the temperature is below 41 °F (5 °C); this will damage the convertible top material."
Now we know why the guy had is top down in that picture included with the "it's always top down weather" It was too cold to put the top up.
It has not detached again but I'm careful to only open and close the top when it's not too cold. Of course that may have nothing to do with the problem.