Getting hot doesn't make them quit until damage is done what I'm saying is there is no overheat shut off sensor on the ATV. There's nothing wrong with the fan running all the time I have mine on all the time too. Quitting after running a short period of time can both be electrical and fuel related. Does it start right back up or does it have to sit and cool before it starts back up? When it quits have you tried removing the cap to see if maybe you hear a giant whoosh of air going into the tank?
Running till they get hot and quitting is a sign of possibly a bad ignition coil or possibly a bad fuel system vent not allowing fuel to flow to the carburetor. There may be other things but those are the most common
Unless you let the bike idle often and run the battery down, having the fan on full time won't hurt anything except wear out the fan motor sooner. You can put a manual switch on it to help save the fan motor and keep the battery fully charged if it idles a lot.
If you'd like to return the fan control to stock you can do that too. Just check the sensor and fan control to make sure those are good. You can add a manual over ride switch to the stock fan control if you wish.