Hi Im reading this with interest as I have been having the same problems, last year Garmin gave me on of the new power cables under warrantee and it worked for 9 months but now has starts again, The pins look fine and there is no play in the mount.
Having tried several things including cleaning the pins ,different power supplys, switched live and direct to battery, I am now wondering if the inline transformer is getting to hot where I have it situated and breaking down, Where do you have yours. I know reg/rectifiers need to be kept cool and this is the same sort of thing but lower voltage, Im going to re situate mine some where cooler and see if this helps.