  Robust qubit memory is essential for quantum computing, both for near-term
devices operating without error correction, and for the long-term goal of a
fault-tolerant processor. We directly measure the memory error $\epsilon_m$ for
a $^{43}$Ca$^+$ trapped-ion qubit in the small-error regime and find
$\epsilon_m<10^{-4}$ for storage times $t\lesssim50\,\mbox{ms}$. This exceeds
gate or measurement times by three orders of magnitude. Using randomized
benchmarking, at $t=1\,\mbox{ms}$ we measure $\epsilon_m=1.2(7)\times10^{-6}$,
around ten times smaller than that extrapolated from the $T_{2}^{\ast}$ time,
and limited by instability of the atomic clock reference used to benchmark the
qubit.
