Although we have no test data or specifications for the components used in a Logger it seems generally accepted that CMOS semiconductor components may have marginal performance above 5 kilorads of Gamma radiation dose. Typically most commercial (i.e non rad-hardened) electronics will fail for doses greater than 10-50krad. Depending on the intensity of the radiation the failure could be just a memory corruption, temporary loss of function or permanent damage/loss of function.
Providing metal shielding for the logger (such as a lead container) will lessen the impact of the radiation.