In these cases, it's almost ALWAYS a cut-off problem of some sort.
It's unlikely the cut-off itself is worn, more likely is simple dirt and fouling around and under the cut-off, or in the action or bolt.
The cut-off is simply a shaped spring. If it's lost it's tension, the screw has loosened, the spring is catching on a burr in it slot, or it's just impacted with fouling, the cut-off will stick "open" and allow a double feed.
I'd suggest doing a full strip and clean of the action, using one of the "Blaster Spray"-type cleaners if you don't feel good about full disassembly yourself.
After THOROUGH cleaning, re-lube and check the cut-off for spring action, and free movement.
Then reassemble and check for proper activation by the action.
Sometimes, it's no more serious than the cut-off screw loosening just enough to allow the cut-off to either stick or shift.
For a full exploded view of the 39-A, look on Gun Parts Corporation's web site.
If worse comes to worse, just replace the cut-off with a new part, being SURE to order one for your era of Marlin.