Measuring the frequency of binary stars in dwarf spheroidal galaxies (dSphs) requires data taken over long time intervals. We combine radial velocity measurements from five literature sources taken over the course of ~30 years to yield the largest multi-epoch kinematic sample for stars in the dSphs Draco and Ursa Minor. With this data set, we are able to implement an improved version of the Bayesian technique described in Spencer et al. (2017, J/AJ/153/254) to evaluate the binary fraction of red giant stars in these dwarf galaxies. Assuming Duquennoy & Mayor (1991A&A...248..485D) period and mass ratio distributions, the binary fractions in Draco and Ursa Minor are 0.50_-0.06_^+0.04^ and 0.78_-0.08_^+0.09^, respectively. We find that a normal mass ratio distribution is preferred over a flat distribution, and that log-normal period distributions centered on long periods ({mu}_logP_>3.5) are preferred over distributions centered on short ones. We reanalyzed the binary fractions in Leo II, Carina, Fornax, Sculptor, and Sextans, and find that there is <1% chance that binary fraction is a constant quantity across all seven dwarfs, unless the period distribution varies greatly. This indicates that the binary populations in Milky Way dSphs are not identical in regard to their binary fractions, period distributions, or both. We consider many different properties of the dwarfs (e.g., mass, radius, luminosity, etc.) and find that binary fraction might be larger in dwarfs that formed their stars quickly and/or have high velocity dispersions.