I'm not sure I understand...
1. was the bike sitting for an extended period or not, before the problem started?
2. How old is the fuel?
3. You say you went down one size on the jets? Which jet (Main, needle clip, pilot}?
Anyway...start with the easy stuff first.
a) Fresh gas, drain the carb float bowls, make sure you have adequate fuel flow from the petcock.
b) Check and clean all your electrical connections, re-seat the high tension wire into the coils and plug caps, check the plug caps for damage, tight connections.
c) Check or preferably clean the air filter, look for oil/water in the airbox
d) Check all the cut out switches, side stand switch, clutch switch, kill switch on right handle bar.
An engine that starts, runs and then dies, sounds like fuel supply. Combustion in the exhaust however, is usually an intermittant ignition problem.
If you can provide some additional detail, I may have some other suggestions. Good luck