Do you have neighbors with kids? Do they lose balls over your fence? Are they coming to pet your puppy? That, or some kid is has a friend that lives behind you and is using your yard as a shortcut. A cheap thing may be buying one of those game cameras at Academy when they are sale. Maybe it'll get a shot of who is doing it. You could also purchase an actual lock for your fence, see if that does anything.
Does the door swing open into your backyard or out? If it's out I'd set up a tripwire and leave a huge pile of your dog's poop in the landing zone for the perp. That'll show them.
"We've met? I don't think so. Where did we meet?" ... Spoiler "We met at your house! Don't you remember."
People are kidding around, but the bottom line is that someone (or a group) is getting into your backyard again and again, going so far as to bust open your gate. It's a drag that your dog is worthless as a deterent, so I'd go the camera route. You can get a fairly cheap system at Best Buy or a big box store. Set that puppy up, get them recorded, and then throw the book at them (or at their parents). Good luck.
like other posters had said: if you cant stay and watch who is it, put some camera to watch it, it could be a normal video camera inside your house, filming the fence.
where do you happen to live? I'll be moving into a new home soon and hope I don't have to deal with a-holes like that. you should set up a camera and post the video and/or pics of the person(or kid) doing that *****. that'll be interesting to see who's trespassing. i can't stand stuff like that.
The sentry gun would be cool, but if you do use it, realize you will probably only get one use out of it, because whoever gets hit with it will probably steal, or destroy it. I would take a day off of work, make it look like you aren't home, and keep a look out. You could also get security cameras installed, but that won't do too much except log proof.
I really do think we know who the intruder is, if you can call him that. <object width="640" height="385"><param name="movie" value="http://www.youtube.com/v/yT2cJg8lut8&hl=en_US&fs=1&"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/yT2cJg8lut8&hl=en_US&fs=1&" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="640" height="385"></embed></object>