it either won't run or run poorly for a short amount then die
Had the same problem.
Also check the fuel cap. When it won't start just open the tank and close it back. If it then starts, means that cap is not properly mounted.
Fuel cap should let the air inside the tank. When fuel is running low air should replace the space inside tank.
If cup is tight and not let air to go, inside tank you got some sort of underpressure. This underpressure holds the fuel inside tank and won't let it flow fluently to the carb.
Solution is to drill a small hole (max 2mm drill) inside the cap. So the air will go inside but fuel won't split.
Drill it on the edge, that gasket will not cover it.
I'll give a pic, cos I'm not sure if I'm unerstandable.

Don't worry, startup631. S.it happens, as people say.
I had to completely dismount my engine when I bought it. (Bought it brand new.)
Click on this ----->
http://motorbicycling.com/showthread.php?p=387312#post387312
Unfortunatly, came brand new without factory sticker on it - because is Chinese made.
No one even checks those eningines in factory before they go out.
Not to say about whole engine kit quality control ....
Chinese factories don't have words "QUALITY CONTROL" in their's dictionaries.
We just have to get use to it, and live somehow with unpredictable Chinese technolgy,
mounted on our bikes.
Pozdrawiam
bluegiant