  Non-Gaussian quantum states, described by negative valued Wigner functions,
are important both for fundamental tests of quantum physics and for emerging
quantum information technologies. However, they are vulnerable to dissipation.
It is known, that the Wigner functions negativity could exist only if the
overall quantum efficiency $\eta$ of the setup is higher than 1/2. Here we
prove that this condition is not only necessary but also a sufficient one: the
negativity always persists while this condition is fulfilled. At the same time,
in the case of bright (multi-photon) non-Gaussian quantum states, the
negativity dependence on $\eta$ is highly non-linear. With the loss of several
photons, it drops by orders of magnitude, hampering its experimental detection.
