  A microelectromechanical oscillator with a gap of 1.25 $\mu$m was immersed in
superfluid $^3$He-B and cooled below 250 $\mu$K at various pressures.
Mechanical resonances of its shear motion were measured at various levels of
driving force. The oscillator enters into a nonlinear regime above a certain
threshold velocity. The damping increases rapidly in the nonlinear region and
eventually prevents the velocity of the oscillator from increasing beyond the
critical velocity which is much lower than the Landau critical velocity. We
propose that this peculiar nonlinear behavior stems from the escape of
quasiparticles from the surface bound states into the bulk fluid.
