This is same problem I had on my gen 1. I found on mine eventually that it was the ignition switch, it was that badly worn that the key would wobble about in the switch causing the engine to misfire or cut out. Try wobbling your key in the switch to see if it is that, all i had to do with mine is touch it and the engine would cut out!
Also check your fuel filter, air filter, kinked fuel pipe,carbs for crap in the float bowls, I also cut back my HT leads 1/2" to make sure they had a good contact. These were all things suggested by guys on here and by the time i had done them all and managed to source another ignition switch the bike was running like a dream when i sold it.