Sadly, very often when one spoke starts to go, its like a virus. They all start to go. This is a symptom of a badly built wheel, where the spokes are too loose. As a consequence, while rolling down the road, spokes start to flex. Think about it – bend metal back and forth and it breaks. In the case of a wheel, this typically happens at the head of the spoke near the center of the wheel.
Having built quite a few wheels in my time, I know how difficult it is to build a good wheel, and most of the standard tools are not designed to handle a small 16" wheel.
If the bike is relatively new, I’d complain to my shop and see what they would do about it. I know what I would do, which is to rebuild and re-true the wheel. For more info on the process, I’d read Jobst Brandt’s book, “The Bicycle Wheel”. Basically, I’m suggesting re-tensioning the wheel, trueing it, pre-stressing it, then trueing it again.