We present a uniform analysis of the atmospheric escape rate of Neptune-like planets with estimated radius and mass (restricted to $M_{rm p}<30,M_{oplus}$). For each planet we compute the restricted Jeans escape parameter, $Lambda$, for a hydrogen atom evaluated at the planetary mass, radius, and equilibrium temperature. Values of $Lambdalesssim20$ suggest extremely high mass-loss rates. We identify 27 planets (out of 167) that are simultaneously consistent with hydrogen-dominated atmospheres and are expected to exhibit extreme mass-loss rates. We further estimate the mass-loss rates ($L_{rm hy}$) of these planets with tailored atmospheric hydrodynamic models. We compare $L_{rm hy}$ to the energy-limited (maximum-possible high-energy driven) mass-loss rates. We confirm that 25 planets (15% of the sample) exhibit extremely high mass-loss rates ($L_{rm hy}>0.1,M_{oplus}{rm Gyr}^{-1}$), well in excess of the energy-limited mass-loss rates. This constitutes a contradiction, since the hydrogen envelopes cannot be retained given the high mass-loss rates. We hypothesize that these planets are not truly under such high mass-loss rates. Instead, either hydrodynamic models overestimate the mass-loss rates, transit-timing-variation measurements underestimate the planetary masses, optical transit observations overestimate the planetary radii (due to high-altitude clouds), or Neptunes have consistently higher albedos than Jupiter planets. We conclude that at least one of these established estimations/techniques is consistently producing biased values for Neptune planets. Such an important fraction of exoplanets with misinterpreted parameters can significantly bias our view of populations studies, like the observed mass--radius distribution of exoplanets for example.
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