Pressure-driven (p-mode) oscillations at the surface of the Sun, resulting from sound waves travelling through the solar interior, are a powerful probe of solar structure, just as seismology can reveal details about the interior of the Earth. Astronomers have hoped to exploit p-mode asteroseismology in Sun-like stars to test detailed models of stellar structure and evolution, but the observations are extremely difficult. The bright star Procyon has been considered one of the best candidates for asteroseismology, on the basis of models and previous reports of p-modes detected in ground-based spectroscopy. Here we present a search for p-modes in 32 days of nearly continuous photometric satellite-based observations of Procyon. If there are p-modes in Procyon, they must have lifetimes less than 2-3 days and/or peak amplitudes <15 parts per million, which defy expectations from the Sun's oscillations and previous theoretical predictions. Target selection for future planned asteroseismology space missions may need to be reconsidered, as will the theory of stellar oscillations.