Life is anything with the capacity for growth, reproduction, functional activity, and continual change preceding death.

While it's interesting to consider sterility as undermining the reproduction part, I think that's more an artifact of the taxonomy. It seems obvious that someone that happens to be born sterile is still alive, because this is more about describing a group than an individual. Humans are alive in a way that rocks are not. The sterile human is still a human, and as a group humans have the capacity for reproduction, even if an individual does not.

Now, all mules are sterile, but it is not a stretch to put the mule in the same taxonomy as its parents. That group clearly has the capacity to reproduce, they're the parents after all. The mule just has the misfortune of being born sterile.

One last semantic argument. The fact that we describe the mule as sterile actually reinforces the idea that it has the capacity for reproduction. It's just broken. If you take a bottle and drill holes in it, you could still talk about its capacity to hold water. It can't hold any water due to the holes, but that doesn't change its existence as a water vessel. You could print a whole batch of these, and they would still be water vessels, that happen to have their water holding be broken.