  We study the hitting properties of the solutions $u$ of a class of parabolic
stochastic partial differential equations with singular drifts that prevent $u$
from becoming negative. The drifts can be a reflecting term or a nonlinearity
$cu^{-3}$, with $c>0$. We prove that almost surely, for all time $t>0$, the
solution $u_t$ hits the level 0 only at a finite number of space points, which
depends explicitly on $c$. In particular, this number of hits never exceeds 4
and if $c>15/8$, then level 0 is not hit.
