We investigate the spectral variability of the Seyfert galaxy Fairall 9 using almost 6 years of monitoring with the Rossi X-ray Timing Explorer (RXTE) with an approximate time resolution of 4 days. We discover the existence of pronounced and sharp dips in the X-ray flux, with a rapid decline of the 2--20 keV flux of a factor 2 or more followed by a recovery to pre-dip fluxes after ~10 days . These dips skew the flux distribution away from the commonly observed log-normal distribution. Dips may result from the eclipse of the central X-ray source by broad line region (BLR) clouds, as has recently been found in NGC 1365 and Mrk 766. Unlike these other examples, however, the clouds in Fairall 9 would need to be Compton-thick, and the non-dip state is remarkably free of any absorption features. A particularly intriguing alternative is that the accretion disk is undergoing the same cycle of disruption/ejection as seen in the accretion disks of broad line radio galaxies (BLRGs) such as 3C120 but, for some reason, fails to create a relativistic jet. This suggests that a detailed comparison of Fairall 9 and 3C120 with future high-quality data may hold the key to understanding the formation of relativistic jets in AGN.