Stellar astrospheres--the plasma cocoons carved out of the interstellar medium by stellar winds--are one of several buffers that partially screen planetary atmospheres and surfaces from high-energy radiation. Screening by astrospheres is continually influenced by the passage of stars through the fluctuating density field of the interstellar medium (ISM). The most extreme events occur inside dense interstellar clouds, where the increased pressure may compress an astrosphere to a size smaller than the liquid-water habitable-zone distance. Habitable planets then enjoy no astrospheric buffering from exposure to the full flux of galactic cosmic rays and interstellar dust and gas, a situation we call "descreening" or "astrospheric collapse." Under such conditions the ionization fraction in the atmosphere and contribution to radiation damage of putative coding organisms at the surface would increase significantly, and a series of papers have suggested a variety of global responses to descreening. These possibilities motivate a more careful calculation of the frequency of descreening events. Using a ram-pressure balance model, we compute the size of the astrosphere in the apex direction as a function of parent-star mass and velocity and ambient interstellar density, emphasizing the importance of gravitational focusing of the interstellar flow. The interstellar densities required to descreen planets in the habitable zone of solar- and subsolar-mass stars are found to be about 600(M/M[middle dot in circle])(-2) cm(-3) for the Sun's velocity relative to the local ISM. Such clouds are rare and small, indicating that descreening encounters are rare. We use statistics from two independent catalogues of dense interstellar clouds to derive a dependence of descreening frequency on the parent-star mass that decreases strongly with decreasing stellar mass, due to the weaker gravitational focusing and smaller habitable-zone distances for lower-mass stars. We estimate an uncertain upper limit to the absolute frequency of descreening encounters as 1-10 Gyr(-1) for solar-type stars and 10(2) to 10(9) times smaller for stars between 0.5 and 0.1 M[middle dot in circle]. Habitable-zone planets orbiting late-K to M stars are virtually never exposed to the severe consequences that have been proposed for astrospheric descreening events, but descreening events at a moderate rate may occur for stars with the Sun's mass or larger.