I might have an idea.
There is a metal bar that runs along the top of all 10 target triggers, or fingers. If 1 or more targets are up at time of reset, this bar is held up by those up targets and does not add extra resistance or weight to the reset sequence. If ALL targets are down, this bar falls and rest on all the triggers and must be pushed up along with the 10 targets.
Maybe this is just enough weight or resistance to stop the assembly short of reset. A thorough examination of this area for binding, dirt, wear, grease and the trigger fingers for wear may help.
You should be able to adjust the reset height also if needed. Also check the reset bar as alot of times the spot welds that hold the lift bar cover on break loose.