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First, this scenario is highly implausible.  Surely the people that went underground intended to pop up again once the war was over.  That means they created some means to monitor the situation on the ground so that they'd know when that was.

However, if you insist, you might be able to hand-wave something about they only have radiation monitors left on the surface.  Those show continuing radiation.  The war may be over, but it might be another few 100 years before the radiation levels get back to habitable levels.  The people underground see the high radiation levels and stay underground.

This could be made a little more plausible (still rather implausible overall) by the pure chance of their location being used as a waste storage area, like what Yucca Mountain was originally planned to be.  However, this was during a war, and there wasn't much careful planning nor execution.  Some of the containment vessels break over the hundreds of years exposed to the elements, due to their hasty (possibly deliberately fraudulent by the contractor) construction in a war zone.  These occasional breakages cause spikes in the monitored radiation levels, leaving the people underground to think that hostile activity is still going on.

Again, this is still quite implausible.  Surely those underground would have geophones and seismometers, and can see when and where there are nuclear blasts within a large radius, possibly over the whole earth.  They would see that the radiation spikes don't correlate to any such activity.

In short, you can handwave a few scenarios, but I don't think any of them will be convincing that the underground people truly forgot.  Even getting fooled by the signals they do see is implausible enough.