when Gollum was dancing with the ring, it was still on Frodo's finger, albeit severed from the rest of Frodo, but technically he was still wearing it as it was on his finger.

this could be analgous to Beren's hand being inside the wolf (whatever it was called) but still holding the Silmaril.

so Frodo was technically still wearing the ring and so may still have had some (reduced) power due to it, which did not cease until his finger was boiled by the fire down below.

just a thought ...