Actually, I have had one or two horns where a rod would gradually unscrew itself like that. (Typically, just one rod out of all of them.) I have no idea why it is sometimes that way. About all you can do is to screw it back in good and tight.
As to spring hooks, you can make a pretty good one out of a paper clip by using a small pair of needle nose pliers to make a tiny hook on the end of the straightened out paper clip. About half the time I can just push the spring out of its hook from the other direction with a small screwdriver, and about half the time I have to reach in there with my homemade spring hook and pull it off its hook.
Once you get that rod screwed back in, you'll probably have no more problems with your small leak.