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We present 1.8 yr of near-daily Swift monitoring of the bright, strongly variable Type 1 active galactic nucleus (AGN) Fairall 9. Totaling 575 successful visits, this is the largest such campaign reported to date. Variations within the UV/optical are well correlated, with longer wavelengths lagging shorter wavelengths in the direction predicted by thin-disk/lamppost models. The correlations are improved by “detrending,” subtracting a second-order polynomial fit to the UV/optical light curves to remove long-term trends that are not of interest to this study. Extensive testing indicates detrending with higher-order polynomials removes too much intrinsic variability signal on reverberation timescales. These data provide the clearest detection to date of interband lags within the UV, indicating that neither emission from a large disk nor diffuse continuum emission from the broad-line region (BLR) can independently explain the full observed lag spectrum. The observed X-ray flux variations are poorly correlated with those in the UV/optical. Further, subdivision of the data into four ∼160 days light curves shows that the UV/optical lag spectrum is highly stable throughout the four periods, but the X-ray to UV lags are unstable, significantly changing magnitude and even direction from one period to the next. This indicates the X-ray to UV relationship is more complex than predicted by the simple reprocessing model often adopted for AGN. A “bowl” model (lamppost irradiation and blackbody reprocessing on a disk with a steep rim) fit suggests the disk thickens at a distance (∼10 lt-day) and temperature (∼8000 K) consistent with the inner edge of the BLR.