There could be several reasons for this. Have you tried;
1) Different sync cables? (you need to set the lens sync to the back sync in, guess the back attaches with firewire to your computer). I had some problematic sync cables
2) Different lens? (the shutter of the 80 could faulty as well). I also had lenses that worked and others that were always a problem. Servicing the lens did prove to be a big help.
3) Is the release mechanism of the Flexbody in good shape? Mine needed CLA (Cleaning Lubrication Adjustment) to trigger the lens shutter in a way that it worked with my CF back.
I would test in this order. I used the Flexbody with a Leaf Aptus17 & a Hasselblad CF39. The Leaf worked flawlessly, the Hasselblad was much more sensitive and needed the Flexbody release mechanism to be in tiptop shape. It also needed to have the right shutter/sync speed set in the back, the Leaf did not have this option.
Not sure whether your H20 works similarly as those 2 but I guess in general it does. Have you got the H20 to fire from the sync? The sync in migh have blown to but I have not yet experienced that problem but did any of the other 3 mentioned above.