The BHO is held up by the magazine follower. There isn't another spring to make it work.
That's why the BHO doesn't function with the magazine swung open.
Try this:
1) Open the magazine up, hold the bolt back, press up on the BHO and "catch" the bolt.
2) Flip the gun over and look at the mag follower and the back of the magazine. Try to picture how the follower should press on the BHO if there are no rounds in the mag holding it down.
3) Close the mag slowly and see if there is somewhere that the follower is hanging up. Why isn't it pressing up on the BHO?
4) Latch the mag shut and then flip the gun right-side up. Look down through the action and find the top of the follower. Use a pencil or pen and press the follower up and down. Is it moving freely? Does it hang up anywhere? Does it come all the way up to hit the BHO?
You should be able to figure out some reason why the follower can't come up and engage the BHO. Might need a little filing if it's binding up.
I suppose your mag spring might not be strong enough to hold it up, but I'd think it wouldn't feed very well if that was the case.
Good luck!
-Sam