We have performed a statistical study of THEMIS spacecraft crossings of the asymmetric dayside magnetopause to test the prediction that the diamagnetic drift of the X-line due to a plasma pressure gradient across the magnetopause can suppress magnetic reconnection. The study includes crossings both when reconnection exhausts were present and when they were absent in the current sheet. When we restrict the survey to the subsolar region (10 < MLT < 14), we find that for low Δβ (the difference of plasma β on the two sides of the current sheet) the majority of reconnection events occurred over a large range of magnetic shears, whereas when Δβ was high reconnection events occurred only for high shears. Furthermore, nonreconnection events occurred primarily in the Δβ-shear regime in which reconnection is predicted to be suppressed, in good agreement with theory. The Δβ-shear condition should have general consequences for the occurrence of reconnection in space and laboratory plasmas.