The lifetime of atomic hydrogen exposed to an intense high-frequency'' linearly polarized laser field has been calculated, in a Sturmian-Floquet approach, for the case where the atom is initially in an excited state with [ital m]=3, 4, 5, or 6, [ital l]=[ital m], [ital m]+1, or [ital m]+2, and [ital n][le]8, for several wavelengths between 455 and 1064 nm. In this range of parameters, the intensity at which the lifetime of the atom reaches a minimum value is given in good approximation by a simple empirical'' law. The lifetime is longer than that predicted by previous approximate Floquet calculations, and its minimum occurs at a smaller intensity. Results for higher-lying Rydberg states are also presented.