We have experimentally studied the magnetic-field dependence of the decay of a Bose-Einstein condensate of metastable ${}^{4}$He atoms confined in an optical dipole trap, for atoms in the $m=+1$ and $m=\ensuremath{-}1$ magnetic substates, and up to 450 G. Our measurements confirm longstanding calculations of the two-body loss rate coefficient that show an increase above 50 G. We demonstrate that for $m=\ensuremath{-}1$ atoms decay is due to three-body recombination only, with a three-body loss rate coefficient of $6.5{(0.4)}_{\mathrm{stat}}{(0.6)}_{\mathrm{sys}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}$ cm${}^{6}$s${}^{\ensuremath{-}1}$, which is interesting in the context of universal few-body theory. We have also searched for a recently predicted $d$-wave Feshbach resonance, but did not observe it.