I agree with Gene there. I'd start with lithium grease lubrication on every joint, pin, etc. you can find. I try to do this annually to ensure smooth operation and reduce strain on the hydraulic system. You'll have to open the top halfway to get all lubrication points.
The other potential problem I'd guess is hydraulic system, potentially low fluid/pressure is preventing the mechanism from opening on its own. I've had a few discussions with Nissan service techs that echoes Gene's comments... they don't have a lot of experience working with these tops. I'd personally be more comfortable going to a convertible top specialist.
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2010 370Z Roadster, Touring 6MT, Pearl White on Black, FI CBE 
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