The two-wire throttle wires typically have a pull and a hold coil as well.
Usually inside the body of the solenoid is a switch that gets activated to disconnect the Pull coil when the solenoid plunger is pulled in completely.
This will disconnect the Pull coil and leave the Hold coil active. This switch activator is visible in the barrel of the solenoid when the plunger is removed.
Be sure it isn't loaded when you look into the barrel!
If the Throttle adjustment is not adjusted correctly and not allowing the Solenoid Plunger to come in fully, excessive heat from the current needed for the Pull Coil can cause damage to the Pull Coil and/or the switch contact inside the end of the Solenoid body.
This will leave only the Hold coil to try to pull the plunger in. It usually wont have enough energy to pull the plunger in and really appreciates it when you give it the little extra nudge of pushing it in. It will be able to hold it after it is in.
Sometimes, if the bolts that hold the end cap on the solenoid can be removed, the contacts of the Pull Disconnect switch inside of the solenoid can be cleaned and put back into service. Typically though, the heat causes damage to the metal tab that holds the contact or the Pull Coil itself has been destroyed.
Best luck for you would be, as Willie pointed out, a low voltage situation when hi-throttle is engaged.
Worse would be having to replace the solenoid.
If you must install a new solenoid, be sure to verify that the plunger is allowed to come all the way in at high throttle. If not, you will be replacing another one in due time.
