  We show that the lifetime of ultracold ground-state $^{87}$Rb$^{133}$Cs
molecules in an optical trap is limited by fast optical excitation of
long-lived two-body collision complexes. We partially suppress this loss
mechanism by applying square-wave modulation to the trap intensity, such that
the molecules spend 75% of each modulation cycle in the dark. By varying the
modulation frequency, we show that the lifetime of the collision complex is
$0.53\pm0.06$ ms in the dark. We find that the rate of optical excitation of
the collision complex is $3^{+4}_{-2}\times10^{3}$ W$^{-1}$ cm$^2$ s$^{-1}$ for
$\lambda = 1550$ nm, leading to a lifetime of <100 ns for typical trap
intensities. These results explain the two-body loss observed in experiments on
nonreactive bialkali molecules.
