We have observed resonant phenomena in the intense-field ionization of argon that do not easily fit into the standard models of above-threshold ionization. High-resolution angle-resolved measurements of the energy region around 6-10 times the ponderomotive potential Up in the ATI electron spectrum show at least three separate series of peaks, each with a distinct intensity threshold for their onset. These series do not shift in energy and have characteristic values of intensity for their appearance, pointing to an intensity-selective resonant enhancement effect. In order to further investigate this phenomenon, we have observed VUV fluorescence photons from the focal region following ionization. Current theories for the creation of high-energy electrons do not seem to explain these phenomena without significant modifications. We discuss possible physical mechanisms and implications for extending the standard model.