What makes it stop working after a while?

Educated guess: Error.

An image stabilization system is like navigation by dead reckoning, in which you figure out where you are based on what you know about where you were, your speed, and changes in direction.

If you're in a car traveling at 60mph for 5 minutes, you know you're going to be about 5 miles from where you started. You might be off a little bit if the car is actually moving at 59 or 61 mph, but you'll end up within easy walking distance of your predicted location, so close enough. But, if you try to predict where the car will be after an hour instead of just 5 minutes, that same small 1 mph error will accumulate over that longer time period, and you'll end up a full mile from your expected location. That may be a larger error than you're willing to accept.

It's the same thing with an image stabilization system. The camera doesn't have an absolute point of reference in space — its accelerometers and gyros can only measure relative displacement and rotation, and although they're very accurate they're not perfect. Moreover, the hardware that moves the sensor or lease element that keep the image stable will have some error of its own. Some error is also inherent in active IS systems due to the fact that the system has to sense movement before it can react, so there's bound to be a delay that causes the system not to track the camera's movement perfectly. Finally, it's likely that no IS system can ensure perfect corner-to-corner image registration while it's compensating for camera motion.

All these errors will accumulate over time. A good IS system might be able to make a handheld 10 s shot better than what you'd get without IS, but not so much better that the manufacturers are willing to claim that it's useful at such a long exposure setting.

In other words: It doesn't stop working; it just reaches a point where it's not sufficiently helpful.