When evaluating the availability of an repairable equipment, it is customary to use its asymptotic (steady-state) value. Recent developments in the field of Information Technology and Telecommunications have shown that the transient regime should not be overlooked, since the availability can decrease below that limit. In a previous work presented in ESREL 2020, a repairable system described by a gamma failure distribution and an exponential repair distribution has been studied. The exact solution for the availability was obtained, exhibiting two regimes in which the minimum availability is indeed smaller than the asymptotic value. We show here that this phenomenon also happens for more general pairs of failure/repair distributions. We provide simple criteria for the occurrence of such a behavior, and apply them to various well-known distributions (lognormal, Weibull, Birnbaum-Saunders, and Inverse Gaussian). We show that replacing the availability by its steady-state value MTTF/(MTTF + MTTR) is not always a safe bet, and that more care should be exercised for the definition of a robust lower bound of the availability, applicable for all times. We conclude by providing methods to assess the true minimum of the availability.