is it the button on the esc or the external one you plug in ? If the former, sounds like a faulty esc/esc switch. You could try contacting CML and see if they can help
https://www.cmldistribution.co.uk/contact
*slight Edit* try both power switches - built in and external
Alternatively, do you have a wifi module or box you could plug into it to check/update the firmware (difficult if it doesnt stay on) and settings to see whats been setup on the esc. Probably a red herring but if the esc is setup for remote off and your tx isnt calibrated, it could be switching itself off that way (I have 4 of these and touch wood, no issues to date)