why is it that motors burn out?

The get hot. They get dirty. They wear out. They burn out.

This is typical of any mechanical device. Moving parts CRAP OUT.

do not allow motor to run longer than designed as over heating causes burn out.

most motor have a temperature fuse that can be replaced as it is mounted on the coil {covered with tape} this will go first and the motor unit is usually ok.

most motors should only be operated 10 minuites continous and allowed to cool 15 minutes. There are many windings of copper in a motor. These windings are kept separated by a type of varnish. When a motor works hard some of the electricity that flows through the windings is turned into heat. If the heat builds up too much some of the varnish burns. The windings short circuit and create more heat. The motor burns up.

Different motors have different specs. There is no rule of thumb on how long they can operate. You can drive Toyota Prius for 500 miles before stopping for gas. That's about 8 hours of continuous use. the rotor is moving, there are contacts (commutators) which have friction on the stators, these wear out, like 1st guy says all moving parts will wear out ..... and they are sometimes overloaded - perhaps because of fouled bearings in whatever they are driving. Overloading will cause rapid overheating.

And as for jimbob92065's "there are contacts (commutators)" ..... unless, of course, they are a.c. motors. All the answers here i agree with except if its an AC motor. I work at a yarn plant as an electrican outside of my tv shop, and there are motors there that have run 24/7 for over a year. thats 61,320 hours.. how do i run those for only 10 minutes???

An AC motor fails due to coils shorting out or bearings failing and locking the shaft down. An load beyond the motors rated capacity(workload not power) will result in a rise in current, thus heat builds up/ melts coils, power shorts to ground.