We present 4.5 and 8 µm photometric observations of 18 cool white dwarfs obtained with the Spitzer Space Telescope. Our observations demonstrate that four white dwarfs with Teᶠᶠ < 6000 K show slightly depressed mid-infrared fluxes relative to white dwarf models. In addition, another white dwarf with a peculiar optical and near-infrared spectral energy distribution (LHS 1126) is found to display significant flux deficits in Spitzer observations. These mid-infrared flux deficits are not predicted by the current white dwarf models including collision-induced absorption due to molecular hydrogen. We postulate that either the collision-induced absorption calculations are incomplete or there are other unrecognized physical processes occurring in cool white dwarf atmospheres. The spectral energy distribution of LHS 1126 surprisingly fits a Rayleigh-Jeans spectrum in the infrared, mimicking a hot white dwarf with effective temperature well in excess of 105 K. This implies that the source of this flux deficit is probably not molecular absorption but some other process.