The implementation of polymer films as cryogenic propellant bladders could mitigate sloshing in a microgravity environment. However, prior research into cryogenic bladders was discontinued in the 1970s due to reportedly high permeabilities of hydrogen and helium through polymer films at cryogenic temperatures. These permeabilities differed from the Arrhenius relation by increasing as temperatures lowered. A hypothesis for this increase was that the comparatively large thermal de Broglie wavelengths of hydrogen and helium at cryogenic temperatures allowed for an increased particulate hopping rate and bulk permeation. Testing of this hypothesis was completed by characterizing the helium permeability of PET, Kapton, Ultem, PEEK, and EVOH polymer films between 190 – 30 K with a calibrated helium mass spectrometer. Results indicate that the permeabilities of each polymer followed the Arrhenius relation until permeation rates dropped below the sensitivity of the mass spectrometer. Below 100 K, the permeabilities were negligible: under this threshold, the design of cryogenic bladders is insensitive to the permeabilities of these films. An explanation for why the historic permeation measurements likely deviated from Arrhenius type behavior is also provided.