Indefinitely. The kind of radiation that causes breeding of hazardous isotopes in local materials is neutron radiation, which is comparatively rare in interplanetary space because free neutrons have a half-life of only 15 minutes. The biggest source of danger in space is high energy proton radiation. Neutrons can, and are, produced in secondary reactions from particle radiation but the flux isn't a sufficient concern to worry about "activation" of materials like water.
Exposure to ionizing radiation can cause formation of free radicals as well as peroxides which could be a concern but the particle fluxes are too low to be a serious concern. At the levels of radiation where it would be a concern the crew would have been exposed to lethal levels of radiation many times over, even with meters worth of water shielding.
It's possible to preserve food with radiation: http://en.wikipedia.org/wiki/Food_irradiation It kills all the living beings inside, but don't make the food radioactive. (It's not exactly the same radiation, but it's very similar.)
(that is the shielding before it is turned into the other kind of shielding)