We present jointly analyzed data from three deep Suzaku observations of NGC 1365. These high signal-to-noise spectra enable us to examine the nature of this variable, obscured AGN in unprecedented detail on timescales ranging from hours to years. We find that, in addition to the power-law continuum and absorption from ionized gas seen in most AGN, inner disk reflection and variable absorption from neutral gas within the Broad Emission Line Region are both necessary components in all three observations. We confirm the clumpy nature of the cold absorbing gas, though we note that occultations of the inner disk and corona are much more pronounced in the high-flux state (2008) than in the low-flux state (2010) of the source. The onset and duration of the "dips" in the X-ray light curve in 2010 are both significantly longer than in 2008, however, indicating that either the distance to the gas from the black hole is larger, or that the nature of the gas has changed between epochs. We also note significant variations in the power-law flux over timescales similar to the cold absorber, both within and between the three observations. The warm absorber does not vary significantly within observations, but does show variations in column density of a factor of more than 10 on timescales less than 2 weeks that seem unrelated to the changes in the continuum, reflection or cold absorber. By assuming a uniform iron abundance for the reflection and absorption, we have also established that an iron abundance of roughly 3.5 times the solar value is sufficient to model the broad-band spectrum without invoking an additional partial-covering absorber. Such a measurement is consistent with previous published constraints from the 2008 Suzaku observation alone, and with results from other Seyfert AGN in the literature.

19 pages, 11 figures, accepted for publication in MNRAS