They definitely DO store the sperm, and at least some of it definitely is viable: several breeders here have had mixed-sire clutches, where one or more babies were sired by a male the that female hadn't seen for several months prior to ovulation. (I want to say "up to six months", but I'm not 100% sure about that.)
Maybe that's a cold-blooded thing. The internal temps are low enough that the sperm just don't die quickly.