First the joke
I'm not a "real geocacher", real geocachers are wimps. I'm an eXtreme cacher!!!!! No paper, no gps, no clothes! Just a bandanna made out of a ripped shirt and a big hunting knife! Imagine if Rambo was a nudist and that's what I look like when I'm on the hunt!!! Once I'm done with community service I'll be out on the prowl again!!!!!
OK now for the serious comment
Since the person who is doing this is taking the time to put the contents in a new box he/she feels some slight connection to the geocaching community. What I'm going to recommend might not work but it's worth a shot.
Add a note all your new caches explaining that you don't understand why someone would work so hard for such a small gain while annoying other people who are just trying to do something because it's fun. Maybe add a suggestion that if the thief really really needs ammo boxes so badly that you would be willing to give him/her some in return for promising to stop stealing the boxes you set-up. Include an email address and the user names of other local geocachers. If you're lucky the person will know some of the people on the list.
I realize what I'm suggesting sounds silly but my dad once worked with someone who stole small hand tools, nothing big, just screwdrivers and wrenches. He could never catch the person who was doing it so he bought a cheap set of tools put them in the top of of his toolbox with a condescending note that (more or less) said "You must be really hard up to need these tools, so here a set you can keep. I'm giving these to you because I don't want to work with people who steal from me." The person must have come across the note and was embarrassed into not stealing.
If that doesn't work you can try skunk scent
http://www.redorbit.com/news/oddities/3529..._on_pine_trees/