I have an '84 VT700, just bought it about 3 months ago.
When I first got the bike it ran pretty good, a little rich but nothing to bad.
That same week there was a rainy day, turns out the bike does not like moisture. When I started the bike my RPM's would not go above 4k, and you could just hear that it sounded like it was struggling. The next day was sunny and all was fine.
Now approx. two months into having the bike the problem started to occur again. (This time however it was normal whether out.) After about 15 min of riding I'll get a big back fire, (one from each cylinder it seems) my RPM's will drop flat, the bike looses power and will continue to run like that until I stop, in which case the engine will cut itself out.
After sitting about 5 or 10 min It will start back up and run until it meets that same point again.
Have tested the coils cold and at the temp when problem occurs and my spark is strong. Can anyone help me out on what could be causing this?

 

CDI is toast. remember, that's 1980's electronics you're dealing with.

 

Yeah, I eventually traced it down to that. Luckily tracing what part of the CDI (Which just prior to you telling I had learned of) hasn't been too big a pain. Trying my spark units at the moment, everything else seems ok. The only other problem which will get replaced is Pulse Generator. It has a very off reading for my rear cylinder.
Thank you for helping confirm that though