I'm not all that in the know on DC motors, as I've mostly done work on larger type AC motors: 1/2 HP to 50 HP three phase motors, and tons of smaller single phase motors, as well as 150-200ish HP 4160V motors. AC motors themselves don't typically burn up, but their windings do. Here are a few of the main reasons they fail:
Environmental factors:
Dust/debris accumulation causing poor thermal dissipation of windings
Moisture accumulation from the environment, particularly in the motor junction box (commonly called a "peckerhead" )
Corrosive atmosphere causing early failure of winding lamination
Poor Installation/Design factors:
Skinned wires somewhere in the power circuit causing an arcing action and increased current and unbalanced power in the windings
Improperly configured overload protection
Improperly sized frequency drives and/or non-inverter duty rated motors (lower fan speeds on squirrel-cage motors don't dissipate heat as designed)
Overload/Contactor failure or an absence of proper circuit protection
Undersized motors circuits for the load (think about motors starting under a full load which isn't it isn't rated for)
Undersized/improperly derated or installed feeder conductors (such as running circuit conductors in separate circuits)
I didn't really touch on mechanical wear as it isn't a common problem. Almost always when a motor fails, especially repeatedly, there is a design issue that needs to be addressed in the system. The things listed above are just things I have witnessed in my experience, and the most common factors, and I have not really included mechanical factors as it is pretty uncommon to have a motor fail mechanically from wear before its designed life-span, but it does happen. Moving parts wear out. Hope this helps.