We have measured the cross sections d2σ/dPTdη for production of isolated direct photons in pp¯ collisions at two different center-of-mass energies, 1.8 TeV and 0.63 TeV, using the Collider Detector at Fermilab. The normalization of both data sets agrees with the predictions of quantum chromodynamics for a photon transverse momentum (PT) of 25 GeV/c, but the shapes versus photon PT do not. These shape differences lead to a significant disagreement in the ratio of cross sections in the scaling variable xT(≡2PT/s√). This disagreement in the xT ratio is difficult to explain with conventional theoretical uncertainties such as scale dependence and parton distribution parametrizations.