Explaining the evidence for surface liquid water on early Mars has been a challenge for climate modelers, as the sun was ~30% less luminous during the late-Noachian. We propose that the additional greenhouse forcing of CO2-H2 collision-induced absorption is capable of bringing the surface temperature above freezing and can put early Mars into a limit-cycling regime. Limit cycles occur when insolation is low and CO2 outgassing rates are unable to balance with the rapid drawdown of CO2 during warm weathering periods. Planets in this regime will alternate between global glaciation and transient warm climate phases. This mechanism is capable of explaining the geomorphological evidence for transient warm periods in the martian record. Previous work has shown that collision-induced absorption of CO2-H2 was capable of deglaciating early Mars, but only with high H2 outgassing rates (greater than ~600 Tmol/yr) and at high surface pressures (between 3 to 4 bars). We used new theoretically derived collision-induced absorption coefficients for CO2-H2 to reevaluate the climate limit cycling hypothesis for early Mars. Using the new and stronger absorption coefficients in our 1-dimensional radiative convective model as well as our energy balance model, we find that limit cycling can occur with an H2 outgassing rate as low as ~300 Tmol/yr at surface pressures below 3 bars. Our results agree more closely with paleoparameters for early martian surface pressure and hydrogen abundance.