We show that the mass-loss rates of active late-type dwarf stars must be significantly lower than recent estimates of up to ~5 × 10-10 M☉ yr-1, 4 orders of magnitude higher than that of the Sun. First, we present aperture-synthesis observations at 3.5 mm of the dMe flare stars YZ CMi and AD Leo, during which neither star was detected at an upper limit of 10 mJy. Although compatible with the tentative detection of YZ CMi at 1.1 mm reported by Mullan and coworkers if the millimeter emission originates from a ~104 K, 300 km s-1 wind with ≈ 5 × 10-10 M☉ yr-1, we show that such a wind would completely absorb the observed radiation from coronal radio flares originating from close to the stellar surface. From this contradiction, we show that the mass-loss rate of any ~104 K wind with solar-wind-like velocities of 300-600 km s-1 must be less than ~10-13 M☉ yr-1, more than 3 orders of magnitude below that inferred by Mullan et al. The corresponding upper limit to a wind at a solar-wind-like temperature of ~106 K is ≈ 10-12 M☉ yr-1, an order of magnitude below the lower limit predicted theoretically by Badalyan & Livshits. Our arguments apply to all classes of stars that display coronal radio flares, implying that the mass-loss rate of active late-type dwarf stars from any ~104 or ~106 K winds with solar-wind-like velocities can be no more than 1 or 2 orders of magnitude, respectively, higher than the solar mass-loss rate of ~3 × 10-14 M☉ yr-1. We show that coronal mass ejections also are unlikely to explain the reported millimeter emission from dMe flare stars, and that the time-averaged mass-loss rate from such events can be no higher than in the case of a steady, spherically symmetric stellar wind.