I'm the opposite. I find putting my top up when garaged keeps it taut and wrinkle free. If I leave it down for a long time it takes some time for the wrinkles to dissappear.

 

It's never good to leave something folded for a long period of time. Having the top up is better for it. This is NOT to say that this is the way it should be since it is a convertible, however, we're speaking only in terms of what's worse - folded down or up (and stretched out).
In the fire service, tarps are always kept folded. It is "standard operating procedure" to re-fold them every few months so the folds don't become permanent. They are folded slightly different each time so that the old folds can straighten out. Ideally, these sorts of things should be stored in big rolls, but failing that, we do what we do.