Wasn’t there a famous incident where it almost misfired because of a Bird or Plane setting it off? (might have been an unrelated incident, but it could’ve started a war)
Also Nukes do require constant maintenance, so they could either have changed the System, or what is equally likely, just let the Nukes rot and use them as a deterrent despite lack of function. The Nukes on their Submarines however are very likely still working.
And his threats about firing Nukes are indeed all fake, he seems to be the kindof guy who waits until the very last possible moment to actually use the Nukes.