We present new X-ray spectral data for the Seyfert 1.9 galaxy NGC 2992 obtained with the Advanced Satellite for Cosmology and Astrophysics (ASCA). These data are combined with archival and published data to outline a 16 year history of flux variability in the X-ray band. We find that, while the 2-10 keV flux has decreased by a factor of similar to 20 in 16 yr, the flux of the Fe K alpha fluorescence line has decreased by only a factor of 2-3, and the inferred amount of Compton reflection is 5 times stronger compared to the continuum than 16 yr ago. From the delay in the response of the Fe K line and inferred Compton reflection to decreases in the continuum flux, we estimate that the reprocessed flux lags the continuum flux by similar to 10 yr, giving a distance of similar to 3.2 pc to the reprocessor. The observed time delay, along with the fact that the Fe K line is narrow (< 6600 km s(-1) FWHM), essentially rules out reprocessing in an accretion disk. This implies the existence of dense, neutral gas with N-H - 10(23)-10(25) Cm-2 within the central regions of the galaxy in addition to a disk, as might be expected for a molecular torus. We find that the flux in the similar to 0.1-4 keV soft X-ray band has decreased by a factor of similar to 15 in 14 yr, similar to the flux in the 2-10 keV band. In addition, the ASCA data, when combined with prior spectral results, imply the presence of a soft excess that is well modeled with partial covering of the nuclear continuum source. We have searched for and found no significant evidence for extended X-ray emission in the ROSAT HRI image of NGC 2992. This lack of extent, coupled with the observed long-term variability of the soft X-ray flux and spectral results for the soft excess, imply that the soft X-ray emission from NGC 2992 is nuclear in origin and is not due to scattering.