DT, do you have an idea who the thieves are? If so, why not confront them face to face.Try persuading them into changing their ways. But be careful, it's not worth getting shot over. Communication is vital, as you mentioned they may not be aware you're allowed in there so a simple, non-threatening conversation would be a start.

Even if you don't know them, perhaps you could do some asking around and find out. The camera idea mentioned before isn't bad either. A local bow shop around here got pics of someone stealing their feeders and they blew up the picture and posted it in their shop.