Gentlemen:
I had the very same issue/problem with a beautiful little BSS "Sporter." My hunting buddy and my gunsmith tried everything but we could not get the little beauty to reliably fire the second barrel. A shooting coach opined that I was "trapping" the trigger and therefore not allowing the mechanism to switch over. He then tried the gun himself and had the same result! We had thoroughly cleaned the mechanism several times, trimmed a bit of wood from the stock....but still the same issue. I then sold the gun in Atlanta.
Tom


Luck is the residue of good intention and hard work.