I don't know that the common swiveling-and-unplugging situation is Gary's problem; both seats are affected.
Doug is right, Gary - why your 12 volt seat operations would affect an alternating current fault interrupter is perplexing. I'd be more inclined to suspect a seat power relay, fuse or breaker, or related component/connection in the 12v electrical bay (Steve mentions) that involves master power to both seats. GFCI's are famous for susceptibility to random current micro-spikes, and Ed Buker enlightened us about some being more so than others - you may need to replace the outlet with a better quality one.
A GFCI fix alone, however, may not be the one needed for your seats.
Joel