  We report on high-resolution Feshbach spectroscopy on a degenerate,
spin-polarized Fermi gas of $^{161}$Dy atoms, measuring three-body
recombination losses at low magnetic field. For field strength up to 1\,G, we
identify as much as 44 resonance features and observe plateaus of very low
losses. For four selected typical resonances, we study the dependence of the
three-body recombination rate coefficient on the magnetic resonance detuning
and on the temperature. We observe a strong suppression of losses with
decreasing temperature already for small detunings from resonance. The
characterization of complex behavior of three-body losses of fermionic
$^{161}$Dy is important for future applications of this peculiar species in
research on atomic quantum gases.
