to rewire or not to rewire

Is it feasible to replace the ign/charging system wiring, Yes, but it will always be a half arsed job that will take as long (quite possibly longer) as replacing the whole wiring anyway. Either buy a new harness and modify it to what you require = moderate cost.  Pay someone to rewire your bike = high cost. Or rewire it your self = cheapest.
You could just bypass the suspect wires with extra ones and route them next to the harness that is already on the bike. That will work but look very messy and could lead to chafeing 
Your bike, your choice.

If you are confident it will fail in the current condition start eliminating components from the battery to the ignition box.  A simple fused wire from the battery terminal past the ignition switch, then to the coil, then to your ignition unit. If it still fails require it. That mess of Connectors under the tank deserves a refresh. PS. If you have a kill switch eliminate that too.
Wiring harnesses are reasonable price, gives you a chance to bring it back to factory spec.
 

If you've still got the old points, I'd put them back.

I had the same symptoms with my Mk 3 Commando. Turned out to be a broken wire to the Boyer Bransden ignition pickup. The wire looked ok, the break was hidden by the insulation.
So is your problem just ignition or are you losing all electics?

... which can sometimes fail when hot. And with the BB system they're in series so if one fails the bike will just stop. A temporary jury rig with direct feed would help eliminate this as a possibility as well.

Of course if this works you can then introduce other suspect components into the mix till you get the problem recurring. I have had no end of trouble tracking down a partial short in the starter motor of my Electra, and spent a lot of time - although not too much money - eliminating various components by substitution of known good ones. Not time or money wasted however as I'm now fairly happy everything is OK.

Wire out kill switch with a short lead under tank, white to white and blue (bypass white yellow to switch) to check it's not like mine and mysteriously cutting out. I like points, with regular dab of high temp grease on cam, and the MK2a Interpol makes use of unmatched zeners with RM23 rotor in a unique arrangement to rectify ac, but I did change most of the electrical pots like capacitor etc but not very expensive, and also replaced some bullets with expensive hex crimp tool. Satisfying and I know what's going on most of the time without much electrical knowledge. Good luck!

As Ian mentioned above coils can fail when hot.  It happened to me last year when road testing a newly rebuilt bike.  It turned out that I had over tightened the clamps holding the coils in place.  When the bike was properly hot one of the coils failed and, being connected in series with the other coil, that was that.  After being recovered I changed the coils and have had no problems since.

Peter Shand gave all the reasonable answers to this one, perhaps you have had the bike 39Yrs but any original wiring is 50 yrs old!! RUBBISH Wiring. With British weather and British wiring 10 years can be enough. The MKII did NOT have the twin zener 'funny' regulator system, only the MKIII and the JPN had that.
The cheapest way and the most instructive way to rewire is to buy my wiring kit (all the right colours and colour chart).
Now another point, it is extremely unlikely that a stator and almost impossible that rotor could cause a sudden or any stop in 'forward motion' If there is any doubt on the rotor, stator or reg/rect, then disconnect them and run on the battery-you have at least 50 or up to 100 miles on the battery. (no lights)
Coils and/or the Boyer Bransden stator plate, can cause sudden stop, but the BB plate is not temperature dependent-just vibration. 
If there is any suspicion of the coils and temperature, then starting the bike from cold and using a hot air gun on the coils, they can be made too hot to touch (70deg and the bike should still run) should show up something.

I had a similar problem with my Mk3 Commando, with the ignition cutting out.  It turned out to be the 45 year old ignition switch.
At the time I did find that turning the key onto the lights position solved the problem, so if your ignition switch is the same as on the Mk3, it may be worth trying this first.  A new switch is a simple fix!

moving the key around often required as light comes on and off. Its new?! I suppose as it hasn't failed on me yet it's fingers crossed..