The holy grail of every nuclear weapons program is the so-called "wooden bomb," that could be thrown on the shelf and left there indefinitely--or, at least, for a very long time.
That goal was never achieved.
Some issues with nuclear weapons: initiators are critical. They supply a burst of neutrons at detonation to make sure that the chain reaction starts. These require materials that emit--or can be made to emit--copious quantities of neutrons. These materials have a rather short half-life. The most reliable neutron source--a deuterium-tritium accelerator--has a problem. Tritium decays into helium-3, which not only doesn't emit neutrons, but actually absorbs a great deal. Relatively small amounts of helium-3 will cause a "fizzle" yield, where the weapon does not generate a nuclear yield.
Tritium, BTW, is much harder to divert than plutonium--because it costs $50,000 a gram. (For you gold bugs out there, that's $1,400,000 an ounce.) Price acts as its own rationing and security mechanism.
High explosives tend to degrade under neutron bombardment. The beryllium tamper will stop MOST, but not all. Some of the compounds that get created by neutron capture have a significantly different pH from the explosives, and will start generating a thermal reaction. This isn't an issue over a year, or two years. But after six years or so, plus however long the weapons were left lying around before that...well, if your stolen nuke starts smoking, start walking away from it in a casual yet rapid manner.
Finally, the plutonium core needs to be remanufactured after about ten years or so--some of the plutonium (Pu-240, the "bad" plutonium that causes predetonation) decays into americium, and that interferes with the overall chain reaction.