Large electromechanical effects in relaxor ferroelectrics are generally attributed to the collective response of an ensemble of correlated, nanometer-sized polar structures induced by chemical and charge disorder. Here, we study finite-size effects on such polar order (i.e., how it evolves when sample dimensions approach the polarization correlation length) in 7-70-nm-thick films of the relaxor ferroelectric PbSc0.5Ta0.5O3. Temperature-dependent polarization studies reveal a linear suppression of the polarization and nonlinearity associated with relaxor order as the film thickness decreases to ≈30 nm. Below this thickness, however, the suppression rapidly accelerates, and polarization is completely absent by film thicknesses of ≈7 nm, despite the continued observation of a broad peak in dielectric permittivity and frequency dispersion. Diffuse-scattering measurements reveal the diffuse-scattering symmetry, and analysis suggests the films have a polarization correlation length of ≈23 nm. Taken together, it is apparent that reduction of sample size and the resulting distribution of polar structures drive suppression and eventual quenching of the electrical response of relaxors, which may be attributed to increasing dipole-dipole and dipole-interface interactions.