What would cause motor mounts to go out on a factory engine?

Motor mounts should last longer than that. They normally break when you put a lot of stress on them, such as hitting a raised railroad crossing going too fast. Sometimes they'll break if there is a lot of vibration in the engine, but you would notice that.

Since they went out that fast, a couple of possibilities are (1) the new mounts didn't get put on right, and one had stress on it causing it to break, or (2) the frame or unibody is bent enough to put stress on the engine mounts, and you'll need some extra washers or spacers added. These are just guesses, and there are surely a lot of other possibilities.

Were the mounts replaced with factory-spec ones? A friend of mine replaced his with aftermarket ones as OEM mounts for his car were not available, and they failed after only a few months due to poor vulcanisation between the rubber and metal parts.

It'd be worth looking for additional items that need to be addressed that could be causing extra strain on your motor mounts.

For example on my vehicle, there are the two front motor mounts underneath the engine. Then there is a third one that depending on who you talk to will call it a rear motor mount, transmission mount or transmission isolator.

Since the engine and transmission are hard mounted to each other, if this rear mount was bad, it could cause additional movement and stress on the front two.

If your suspension needs new shocks, bushings, etc you are going to have more movement in the vehicle and then items such as @xpda mentioned of rail road tracks are going to transfer into the wrong places, potentially your motor mounts.

Make sure the squeaking is coming from the motor mounts. I had an issue that I thought was the motor mounts and so I replaced them. The rattling was gone. However over time it came back and got worse. Then the balance shaft broke into pieces and it was clear that the shaft was the problem from the beginning.

Were all of the engine mounts replaced or just the broken ones? It's possible that you're replacing engine mounts whilst not replacing other engine mounts which could be making your motor slightly vibrate which will further stress the other mounts and break them. It takes just one bad mount to break the rest of them.

Are you thrashing your car by any chance? Burn-outs, hard breaking and accelerating, if it's a manual hard gear changes can also break your mounts earlier.

Possible that the valve cover leak was allowing hot oil to drip on the motor mounts shortening their life and as Dwayne states maybe only the broken one was replaced.

Are your mounts located directly near your exhaust manifold? Do they have a heat shield? The rubber can dry and crack due to the heat from the exhaust manifold if not properly insulated/protected from the heat. On my 944, there is a small tin heat shield that protects the mounts from the manifold. Leaking oil onto the mounts will also accelerate their wear, as again on my 944 I had a valve cover (or rather, camshaft tower) oil leak which leaked oil on the motor mounts, which again causes accelerated wear. You should also be careful about the replacement mounts - some OEM mounts may have hydraulic dampening (filled with fluid) but cheap third-party replacement mounts might be solid rubber instead and much more prone to early failure.