The recent discovery of ``ultra-hot'' ($P < 1$ day) Neptunes has come as a surprise: some of these planets have managed to retain gaseous envelopes despite being close enough to their host stars to trigger strong photoevaporation and/or Roche lobe overflow. Here, we investigate atmospheric escape in LTT 9779b, an ultra-hot Neptune with a volatile-rich envelope. We observed two transits of this planet using the newly-commissioned WINERED spectrograph ($R\sim68,000$) on the 6.5 m Clay/Magellan II Telescope, aiming to detect an extended upper atmosphere in the He 10830 A triplet. We found no detectable planetary absorption: in a 0.75 A passband centered on the triplet, we set a 2$\sigma$ upper limit of 0.12% ($\delta R_p/H < 14$) and a 3$\sigma$ upper limit of 0.20% ($\delta R_p/H < 22$). Using a H/He isothermal Parker wind model, we found corresponding 95% and 99.7% upper limits on the planetary mass-loss rate of $\dot{M} < 10^{10.03}$ g s$^{-1}$ and $\dot{M} < 10^{11.11}$ g s$^{-1}$ respectively, smaller than predicted by outflow models even considering the weak stellar XUV emission. The low evaporation rate is plausibly explained by a metal-rich envelope, which would decrease the atmospheric scale height and increase the cooling rate of the outflow. This hypothesis is imminently testable: if metals commonly weaken planetary outflows, then we expect that \textit{JWST} will find high atmospheric metallicities for small planets that have evaded detection in He 10830 A.
Comment: 11 pages, 3 figures, accepted for publication in ApJL