Fission-fusion devices (H-bombs) require tritium refreshment, that is true. Fission devices (A-bombs--think Fatman and Little Boy) do not employ a second stage, where the tritium is used. They would be very shelf-stable, as long as the batteries were maintained.
HYDROGEN BOMBS (i.e. thermonuclear fusion bombs) have to be maintained, as the tritium component has a relatively short half-life (12 years, as I recall). Not so for fission weapons (which is what Saddam-the-Insane is likely to have). The nuclear isotopes that "go boom" (either uranium (U-235) or plutonium (Pu-239)) have half-lives in the thousands of years range. I suspect that if there is a component that needs replacement on fission weapons, it will be the chemical explosive that triggers the fission reaction.