The dog probably does not get enough stimulation and exercise, so when he gets free, he does not want to give it up and come back. The problems rarely come from the dogs, but from their owners. Unless they are not spaded or neutered, Great Danes, which belong to molossers, are not roamers. Ours would never, ever leave the yards and had perfect recall. And passed two to three years old, they settle and become very calm dogs. Not at all like scent hounds which are hard to train, notorious roamers and will take off on a scent and never look back. I would suggest getting help and advice training the dog before he gets into serious troubles. With a dog that large and powerful, absolute control over the dog is not a luxury, but a necessity. In my neck of the wood, if after a few warnings, your dog is caught roaming, harassing the livestock, and chasing the wildlife, it is just plain shot and its perfectly legal. And the owners have only themselves to blame. Its their fault but its the dog that pays. Just my two cents...