It is well known that successive observations of the instantaneous state of a decaying system lead to a modified decay law. In the limit of infinitely frequent observations, the modified lifetime becomes infinite (“Zeno's paradox”). We study here the behavior of decaying systems under continuous rather than successive observations. Such continuous observation is achieved by a permanent coupling of the decaying system to a counter, which is sufficiently sensitive to the presence of the decay products. For two explicitly soluble models (...) we obtain a result very similar to Zeno's paradox: The observation again strongly modifies the decay law, and prevents the decay completely in the limit of a perfect (i.e., infinitely sensitive) counter. Like Zeno's paradox, however, this “watchdog effect” is not very likely to be detected in actual experiments, e.g., with radioactive nuclei. (shrink)