there could be two problems here,
First check the speed pot, when it stops try pressing the throttle lever in the upwards direction as you push forward, if it responds then your scooter requires a new speed pot.
Check the brushes on the motor, make sure they can move inside, if they are jammed this will cause the problems you mentioned, check the battery connection are clean and tight.
Regards
gewizrepairs.co.uk, December 2009