Uranium 235 has a half-life of 71 million years and Pu239 has a half-life of 24,400 years, so an age of a few hundred years would not seriously deplete either core.
There may be other isotopes such as polonium (6 months) or tritium (about 12 years) that would limit life. If I were a weapons designer I'd design them so that they all required some depot level maintenance, to cover just such a circumstance of losing physical control of the devices. On the other hand a perverse engineering group could design them to last 50 or 100 years, just in case they had to survive a long time "underground" and several disarmament treaties.
In a world without strategic nukes for retaliation a small stockpile of little bombs would carry considerable weight.
If I remember correctly our old Davy Crockett had some limited life components.