Coronal mass ejections (CMEs) are powered by magnetic energy stored in electric currents in coronal magnetic fields, with the pre-CME field in balance between outward magnetic pressure of the proto-ejecta and inward magnetic tension from confining overlying fields. In studies of global, current-free coronal magnetic field models --- Potential-Field Source-Surface (PFSS) models --- it has been reported that model field strengths above flare sites tend to be weaker in when CMEs occur than when eruptions fail to occur. This suggests that potential field models might usefully quantify magnetic confinement. An implication of this idea is that a decrease in model field strength overlying a possible eruption site should correspond to diminished confinement, implying an eruption is more likely. We have searched for such an effect by {em post facto} investigation of the time evolution of model field strengths above a sample of 10 eruption sites, which included both slow and fast CMEs. In most events we study, we find no statistically significant evolution in either: (i) the rate of magnetic field decay with height; (ii) the strength of overlying magnetic fields near 50 Mm; (iii) or the ratio of fluxes at low and high altitudes (below 1.1$R_{odot}$, and between 1.1--1.5$R_{odot}$, respectively). Instead, we found that overlying field strengths and overlying flux tend to increase slightly, and their rates of decay with height become slightly more gradual, consistent with increased confinement. Since CMEs occur regardless of whether the parameters we use to quantify confinement are increasing or decreasing, either: (i) these parameters do not accurately characterize confinement in CME source regions; or (ii) systematic evolution in the large-scale magnetic environment of CME source regions is not, by itself, a necessary condition for CMEs to occur; or both.
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