Mine doesn't stay up either and since I don't have 3 hands I used a clamp with a shot bag strap around it for weight to keep it open. The top left edge of this picture shows the clamp and strap around it. Off frame is a shot bag laying on the floor that provided enough drag resistance to keep the lid open.
I'll probably cut a stick or something one of these days to use as a prop and just leave it on top of the batteries for future battery fills.
When I saw this thread title, my thoughts or hopes was to open it and see a battery box mod that allowed 2 6V GC batteries to be stored.