Understanding variation in species occupancy is an important task for conservation. When assessing occupancy patterns over multiple temporal seasons, it is recommended to visit at least a subset of sites multiple times within a season during a period of closure to account for observation biases. However, logistical constraints can inhibit re-visitation of sites within a season, resulting in the use of single-visit multi-season occupancy models. Some have suggested that autocorrelation in space and/or time can provide “fractional replication” to separately estimate occupancy probability from detection probability, but the reliability of such approaches is not well understood. We perform an extensive simulation study to assess the reliability of estimates from single-visit multi-season occupancy models under differing amounts of spatial and temporal autocorrelation (“fractional replication”). We assess model performance under both correctly specified models and multiple forms of model mis-specification, and compare estimates from single-visit models to models with varying amounts of within-season replication. We also assess the reliability of single-visit models to estimate occupancy probability of ovenbirds (Seiurus aurocapilla) in New Hampshire, USA. We found less bias in estimates from single-visit occupancy models with long-range spatial autocorrelation in occupancy probability compared to short-range spatial autocorrelation when the model is correctly specified. However, under certain forms of model mis-specification, estimates from single-visit multi-season occupancy models were biased and had low coverage rates regardless of the characteristics of the “fractional replication”. In contrast, models with varying amounts of additional replication were robust to model mis-specification. Our findings suggest that “fractional replication” cannot replace true replication in terms of occupancy probability identifiability and that researchers should consider the potential inaccuracies when using single-visit multi-season occupancy models. We show that a little true replication can go a long way with even 10% of sites being revisited within a season leading to reasonably robust estimates even in the presence of extreme model mis-specifications. When possible, we recommend performing multiple within-season visits to at least a subset of spatial locations or integrating single-visit data with other data sources to mitigate reliance on parametric assumptions required for reliable inference in single-visit multi-season occupancy models.