HI Colsie
As well as the above , some ESC's can be picky regarding the tranny settings, requiring, say, the reverse setting to be used on the tranny.
Some ESCs require you to do a set up at first use and you should follow the instructions, you can perform this procedure at any time and it may help sort out any problems. The other Important step is to make sure that your tranny controls are all at neutral at switch on, and the transmitter should always be switched on before the receiver and not switched off until after the receiver.
If whilst on the bench, the motor is achieving full speed before cutting out then you need to reduce the stick forward travel. You may be able to do this by using the trim control. if this works you will need to reset the ESC to the new central dead band, by leaving the trim in the new position and resetting the ESC. You will need to use this trim position at all subsequent switch-ons.
I am assuming you have a basic TX without additional controls to adjust the end point, but please ask if you need help. 😀

HI Gary
if your running brushless, some of the esc don't give you full reverse, so it might be that. Change the reverse switch on the tx, if you get 3/4 on both you are drawing the same on both , it would seem you are drawing too many amps. Hope this helps.
regards
Dave

Could be you are overloading the speed control at full throttle so it's cutting the power, I would presume the reverse does not give full throttle so the problem does not arise.
What is the size amperage wise of your speed control.
A few more details of your set up would help Ie battery voltage, motors, prop diameter