I don't have confirmation that Land Mines or Bear Traps are or are not Persistent, but it seems to me that on a Persistent server that when you place land mines they should stay after a reset, right?
Well assuming that's the intended outcome it is not so. When I plant a Land Mine OR Bear trap, they despawn after a server reset. I have tested and confirmed this four times so far in a matter of months, the last time approximately one week ago - It's very rare that I find either of them.