About the worse thing you can do to any electric setup is attempt long runs without any cooling air. How long is "a short time" ?

It's most likely that the battery is losing voltage and kicking in the LVC (low voltage cutoff) on the ESC. This may be overheating of battery or esc. It's also possible the battery is not fully charged. The one thing it isn't is over current on the ESC because that battery will never deliver more current than that ESC can take.

What type of battery is it and how are you charging it ?

Whatever you are probably better off going flying.