  Detailed modeling of the recent star formation histories (SFHs) of
post-starburst (or "E+A") galaxies is impeded by the degeneracy between the
time elapsed since the starburst ended (post-burst age), the fraction of
stellar mass produced in the burst (burst strength), and the burst duration. To
resolve this issue, we combine GALEX ultraviolet photometry, SDSS photometry
and spectra, and new stellar population synthesis models to fit the SFHs of 532
post-starburst galaxies. In addition to an old stellar population and a recent
starburst, 48% of the galaxies are best fit with a second recent burst. Lower
stellar mass galaxies (log M$_\star$/M$_\odot<10.5$) are more likely to
experience two recent bursts, and the fraction of their young stellar mass is
more strongly anti-correlated with their total stellar mass. Applying our
methodology to other, younger post-starburst samples, we identify likely
progenitors to our sample and examine the evolutionary trends of molecular gas
and dust content with post-burst age. We discover a significant (4$\sigma$)
decline, with a 117-230 Myr characteristic depletion time, in the molecular gas
to stellar mass fraction with the post-burst age. The implied rapid gas
depletion rate of 2-150 M$_\odot$yr$^{-1}$ cannot be due to current star
formation, given the upper limits on the current SFRs in these post-starbursts.
Nor are stellar winds or SNe feedback likely to explain this decline. Instead,
the decline points to the expulsion or destruction of molecular gas in
outflows, a possible smoking gun for AGN feedback.
