Sounds like an opportunity to set up a "honey pot", using a game cam that sends back images of the thieves stealing an item of value used to lure them in.

That totally sucks though, and is one of the reasons I have never purchased a cottage or property that contains something of value I have to worry about. I have anxiety problems enough without adding to the heap. I would even worry if it were on my own place with me in it at the time!

If they hadn't cut the locks, there is nothing to prevent them from tin-snipping the walls or using a wrecking saw to go through a wall rather than trying the door. Your best defense is going to be catching the SOBs.