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One or both of the spring loaded cables, that are suppose to tug on the front of the top, must be broken. This is a very common problem actually and I have replaced many for this exact problem. Part of the convertible top headliner has to be removed in order to replace them. Ill look up the part# *****
Above is a link on actually performing the repair if interested. I'm still looking up the part#, I'll post it here soon.
Part# ***** 770 18 65. I would replace both of them and not just the one that broke
I would expect a shop to charge no more than 2 hours labor and parts are about $100-150 each if you decided to go that route.