As polio-endemic countries move towards elimination, infrequent first infections and incomplete surveillance make it difficult to determine when the virus has been eliminated from the population. Eichner and Dietz [American Journal of Epidemiology, 143, 8 (1996)] proposed a model to estimate the probability of silent polio circulation depending upon when the last paralytic case was detected. Using the same kind of stochastic model they did, we additionally model waning polio immunity in the context of isolated, small, and unvaccinated populations. We compare using the Eichner and Dietz assumption of an initial case at the start of the simulation to a more accurate determination that observes the first case. The former estimates a higher probability of silent circulation in small populations, but this effect diminishes with increasing model population. We also show that stopping the simulation after a specific time estimates a lower probability of silent circulation than when all replicates are run to extinction, though this has limited impact on small populations. Our extensions to the Eichner and Dietz work improve the basis for decisions concerning the probability of silent circulation. Further model realism will be needed for accurate silent circulation risk assessment.