We present a study of the orbital light curves of the recurrent nova IM Normae since its 2002 outburst. The broad eclipses recur with a 2.46 hour period, which increases on a timescale of 1.28(16)x10^6 years. Under the assumption of conservative mass-transfer, this suggests a rate near 10^-7 M_sol/year, and this agrees with the estimated /accretion/ rate of the postnova, based on our estimate of luminosity. IM Nor appears to be a close match to the famous recurrent nova T Pyxidis. Both stars appear to have very high accretion rates, sufficient to drive the recurrent-nova events. Both have quiescent light curves which suggest strong heating of the low-mass secondary, and very wide orbital minima which suggest obscuration of a large corona around the primary. And both have very rapid orbital period increases, as expected from a short-period binary with high mass transfer from the low-mass component. These two stars may represent a final stage of nova -- and cataclysmic-variable -- evolution, in which irradiation-driven winds drive a high rate of mass transfer, thereby evaporating the donor star in a paroxysm of nova outbursts.