In my opinion, it is far too dangerous to keep nuclear weapons on foreign soil. What if the militia in that country found a way to break in and steal them? Then we would be at risk to be blown up by our own weapons! I just can't see justifying the storage of these dangerous weapons on soil where we are at a disadvantage. The natives know the area better, and could be better prepared to attempt to steal them.
Nuclear weapons have the ability to literally destroy the world and they must be stored in a way that does not subject them to seizure. Storing them on a military installation in a foreign country is not necessarily safe. Military bases can be overrun by enemies, and this danger is ever present in foreign countries.
I'm not sure of the tactical reasons if any for storing US nuclear weapons at a base in a volatile country. Anything outside our jurisdiction could be vulnerable to seizure and to being deployed by other countries at us or at our allies. It doesn't seem like a good idea to risk the possibility that a change in regime could result in our own weapons be stolen or used against us.
If an enemy were to get the upper hand and take hold of a region with U.S. nuclear armaments positioned in it, then they would have them. I understand that U.S. forces regularly give security and safety for the nuclear weaponry. It is still too much of a risk though.