could be the battery and to find out put the headlights on and see if it conks out like it does when you have the indicators running .
you might have a charged battery at the time you go out but it may lose charge after a while hence the engine missing .
check the alternator is working etc .
on my leader i had problems with the indicators not working properly and found the wires behind headlight were the area of trouble along with the horn wire as well , basically the wiring loom runs close to the the forks and tops of suspension units and can rub and get caught up when you turn the forks .
not sure if only arrows use plastic caps on top of suspension and leader doesnt but my leader is an early 1958 one and has no caps and this leaves the shock absorber threads exposed and able to catch the loom .
i had 4 wires chafed or broken behind the headlight due to this and had to repair them .
it can be a bit of a job to get at the wiring to work on it but the headlight comes out easily so you can look at the wiring .
years ago when i used the bike as a teenager it conked out on me one night in 1982 and was missing an coughing etc and eventually stopped dead
that turned out to be the alternator gone and needed replacing , i am now riding the bike again and using the alternator that was fitted back then and it is ok .
my AJS dynamo failed a while back and i didnt know about it until the lights went dead after i pushed the horn button one day , then found oil in the dynamo , so i rebuilt it and all is fine now .
measure your voltage output at the centre terminal out of the rectifier on the leader and see if it is providing the right voltages , if using a analog meter you will see the needle swinging between about 5 and 8 volts .
good idea to fit in line fuse of about 10 amps in the negative line from the battery just in case you get a short anytime .
look under handlebars as there are wires that pass through holes in the top of cubby box and also down inside cubby box where the steering lock is as the wires are close there too for catching ..
hope you sort it without much trouble