It seems unlikely to be a brushless 12 motor with integrated controller; they are more expensive at present.
I suspect that instead, you have an EMC problem with the cheap PWM controller and a nasty brushed motor, emi-wise. EMI from the motor is glitching the MOFET gate or gate controlling circuitry, thus you see full speed until failure. Capacitors at the motor, and a common mode choke might solve it fairly cheaply. A better designed PWM controller might be able to handle it. If your 12V supply is also full of EMI, that should also be addressed via passive filtering since the controller may not handle that well either.
MOSFETs have amazingly low "on" resistance so can handle a huge load in a single small package. They do have some serious issues with EMI; their gates are voltage controlled and are much more susceptable to glitching than older bipolar transistors which are current controlled.
The solution to avoid glitching is suppression at the source (motor), but also to use a very low resistance gate drive (1-10 ohm). Many cheap electronics will not in order to save cost.
Solving the problem at the source is a cost effective solution as it prevents the same EMI from damaging or cause intermittent faults of other connected electronics. For a "junk box" filter for this motor, I'd start with 0.0-1 uF ceramic, and 10-100 uF electrolytic, and a 3+ mH common mode choke rated for your max current or better.