whitish tan looking

 

Hmm...that you have to hold the throttle open to restart it would indicate a rich mixture. You can find out for sure by opening the choke cable slightly when it's starting to die, if it makes it worse, it's rich for sure. It could be just an adjustment problem, such as idle speed or mixture screw or a combination of both. You need to follow the Honda procedure for setting them. If you don't know the history of the machine, somebody could have drilled out the slow jet in a ham handed attempt to clean it. Also check carefully the slow jet air bleed holes on the jet, and the air bleed circuitry in the body of the carb. I think it gets its supply of air underneath the carb slide diaphragm, and also goes through an air cut valve, then down to the slow jet itself. You may want to test the air cut valve itself, in conditions of high intake manifold vacuum, that is when you close the throttle at high speeds, it cuts air to the slow circuit, to avoid decel popping and backfiring. If this device were stuck closed, ( can't say I've seen one fail yet) it would run rich. You may also want to try a new spark plug, in case yours is on the verge of fouling.

 

I think you just have a misadjusted carb,
carb cleaning
Reading this may help you.

 

have you ever done anything with the air filter.
or did you have it standing up on the rear rack washing it or something like that
try removing the air filter and see how it runs and starts sounds like you might want to wash it out and reoil just don't use motor oil either some gear oil or get the honda air filter oil