An 8 month monitoring campaign on the Seyfert 1 galaxy Fairall 9 has been conducted with the International Ultraviolet Explorer in an attempt to obtain reliable estimates of continuum-continuum and continuum--emission-line delays for a high-luminosity active galactic nucleus (AGN). While the results of this campaign are more ambiguous than those of previous monitoring campaigns on lower luminosity sources, we find general agreement with the earlier results: (1) there is no measurable lag between ultraviolet continuum bands, and (2) the measured emission-line time lags are very short. It is especially notable that the Ly alpha + N V emission-line lag is about 1 order of magnitude smaller than determined from a previous campaign by Clavel, Wamsteker, & Glass (1989) when Fairall 9 was in a more luminous state. In other well-monitored sources, specifically NGC 5548 and NGC 3783, the highest ionization lines are found to respond to continuum variations more rapidly than the lower ionization lines, which suggests a radially ionization-stratified broad-line region. In this case, the results are less certain, since none of the emission-line lags are very well determined. The best-determined emission line lag is Ly alpha + N V, for which we find that the centroid of the continuum--emission-line cross-correlation function is tau cent ~ 14--20 days. We measure a lag tau cent <~ 4 days for He II lambda 1640; this result is consistent with the ionization-stratification pattern seen in lower luminosity sources, but the relatively large uncertainties in the emission-line lags measured here cannot rule out similar lags for Ly alpha + N V and He II lambda 1640 at a high level of significance. We are unable to determine a reliable lag for C IV lambda 1550, but we note that the profiles of the variable parts of Ly alpha and C IV lambda 1550 are not the same, which does not support the hypothesis that the strongest variations in these two lines arise in the same region.