My Vire 7 does the same, will die if I throttle down too much, occasionally will lose power, the rpm's will drop and throttling up won't help.
We changed out the entire fuel delivery system when we found rust in the fuel filter (the original tank was there, flaking away) including vent line, fill line, etc.
Our performance is better, but not healed.
I'm going to be setting the idling screw up this weekend, I'm pretty sure the mixture is just too rich and the engine is flooding out. (when I close the throttle all the way down, it's almost a sure death)
I have not yet had the carburetor rebuilt.. that's next on the list.
1973 O'Day 27