NoTimeToPlay

I had similar symptoms with my XJ600 and spent ages not finding electrical problems. I had also checked the fuel cap vent (so I thought) but therein actually was the problem. The cap has a diaphragm valve (maybe a safety seal in the event of a fall?) I winkled out the diaphragm and have never had this problem since.

My Diversion suffered similarly: I traced the fault, after going through carbs, ignition etc, to a blocked vent in the tank cap. There is a membrane valve in the cap which I guess is intended to prevent the vent leaking fuel after an accident (or possibly rain ingress) but it was working rather too well! I hesitate to recommend my course of action which was to remove the valve but there have been no problems since. Ride safely.

I cannot offer anything other than sympathy because I have a similar problem with my 10yr old 10,000 miles SJ600. Simply waiting for it to cool (typically 20 minutes) after cutting out makes it good for another 50 or so miles except in traffic when 7 miles is the best between cutting outs. I am not entirely convinced it is simply temperature related because it does much the same in the wet - slightly more annoying! I hope these symptoms may help with your diagnosis too.