Heritage special keeps cutting out

Hi. I have a 1982 US import heritage special which my partner owned for a couple of years and I persuaded him to sell to me. HOWEVER , since it became mine it has developed an annoying fault. It will run fine for many miles and then suddenly it will fail as if it has fuel starvation...often for a couple of beats and then pick up. it rarely does this if john rides it. Revving or ticking over in neutral it does fine and only cuts out under load when in gear. Sometimes putting it into gear makes it cut out. Even it will do it every 100 yards cutting out on me and if i get off and he takes it for a blatt then it behaves perfectly! Revving the nuts off it helps to keep it going. Letting the revs drop or coasting to a halt e.g. at junctions it is likely to cut out. When cold it will restart straight away. When hot it sometimes refuses.
I replaced the coils but it still does it. The bike shop found a loose fuse wire under the seat which makes some sense as I am a foot shorter than John so he sits on a different part of the seat. I also have more problems when carrying camping gear in throw over panniers. the shop had it idling perfectly but then it cut out when the mechanic rested his hand on the fuse box/ wiring loom. He replaced the fuse holder. We though it was sorted but it cut out four times on me in the 6 mile ride home. any suggestions what else to check for? Thanks. Getting frustrated no summer weekend rides!

Welcome aboard!
You may have a couple of issues going on.
IF it were mine I'd be checking the balance on the carbs, making sure they were synched. That could give you an issue when slowing down to a stop....also you mentioned keeping her revved seems to help and hard starting when hot - possible fuel/carb issues.
On the fuses - some replace the fuse holder with the spade type inline fuses and then there are some that have kept the original holder with no issue. Might start her up and then wiggle/move the connections at the holder and see what happens.
On the US Heritage models, '82 and '83 there are a couple of safety relays. The neutral safety switch and the side stand safety switch. These can sometimes act up, but not likely to be intermittant. I personally removed/bypassed the ones on my '83 with the help of a decent manual and some simplified wiring schematics. It's a challenge but can be done.

Thank you. I think the poor thing has been fiddled with by previous owners as the side stand switch is gone but she still has the "won't start unless its in neutral" switch. She also has a switch to turn off the day riding lights as I am in the UK so don't need them all the time. I guess its a dry joint or corroded wire somewhere under the seat which will be a bugger to find. when she runs sweetly she will hold 70 mph and above with no problem. When she's playing up its hiccup drop off backfire stumble stop. I also have only one fuel tap fitted to the tank, there is no balance pipe. Fuel starvation does not seem to be the problem as I get the backfire and can get high speeds....it's something about igniting the fuel that is misbehaving. First guess was coils breaking down but replacing them didnt fix it.

A Volt/Ohm meter with a continuity tone is invaluable in troubleshooting the loom.
One of the best suggestion on a new to you xs is to break loose all the connectors, clean 'em up, add a smidgen of Di-electric grease and snap 'em back together. Also check all the earth to frame connections. You may come across an obvious problem, maybe not, but it's something that should be done. Note that there are no two multi connectors in the headlight bucket that could be switched accidentally, but watch the single bullet plugs.....black can sometimes look like dark brown. Do one bullet at a time to avoid mixing colors.