After a little more searching on the internet, I’m discovering that one of the most probable causes may be overheating. It is a second hand Kinect and I really have no idea how old it is and how much dust it may have built up. So, on my next attempt I blew into the fan to help clear it out. The Kinect did still die but it actually seemed to last longer.
My next course of action will be to disassemble the unit and give it a thorough clean.
I may be barking up the wrong tree so if anybody knows of the solution, please let me know otherwise I will update if this does indeed solve the issue.