Balanced half-sample (BHS) variance estimation is a popular technique among survey statisticians, but it has limitations. These limits are studied theoretically through a model-based approach and illustrated with simulations using artificial and real populations. In the fully balanced case, under a model often used for stratified, clustered populations, BHS produces a model-unbiased variance estimator for only one member of a broad class of estimators of totals. Another implementation of BHS variance estimation in large, complex surveys is to use partial balancing or grouping of strata to reduce the number of resample estimates that must be calculated. Instead of selecting a fully balanced, orthogonal set of half-samples, strata are combined into groups and a set of half-samples only large enough to be balanced on the groups is selected. For two-stage cluster samples either with or without poststratification this leads to an inconsistent variance estimator.