  Luminous infrared galaxies (LIRGs), the most extreme star-forming galaxies in
the nearby (D$<$30 Mpc) Universe, show a notable X-ray emission deficiency (up
to a factor of $\sim$10) compared with predictions from scaling relations of
galaxy-wide high mass X-ray binary (HMXB) luminosity with star-formation rate.
In the nearby ($\approx$20 Mpc) LIRG NGC 7552, the majority of the IR emission
originates in a circumnuclear starburst ring, which has been resolved into
several discrete knots of star formation. We present results from recent
Chandra observations of NGC 7552, which reveal significant deficits in the 2-7
keV X-ray luminosities from two of the most powerful star-forming knots. We
hypothesize that the expected luminous HMXB populations in these knots are
either (1) obscured by very large column densities or (2) suppressed due to the
knots having relatively high metallicity and/or very young ages ($\lesssim$ 5
Myr). We distinguish between these possibilities using data from recent NuSTAR
observations, whose sensitivity above 10 keV is capable of uncovering heavily
obscured HMXB populations, since emission at these energies is more immune to
absorption effects. We find no evidence of a heavily obscured HMXB population
in the central region of NGC 7552, suggesting suppressed HMXB formation. We
further show that metallicity-dependent scaling relations cannot fully account
for the observed deficit from the most powerful star-forming knots or the
central region as a whole. Thus, we suggest that recent bursts in local star
formation activity likely drive the high $L_{\rm{IR}}$ within these regions on
timescales $\lesssim$ 5 Myr, shorter than the timescale required for the
formation of HMXBs.
