I would start calling Animal Control everytime the dog doesn't have water and shelter, and take lots of pictures while still on your own property so you don't get yourself in trouble. Report him right away if you see him beating the dog and try and get pictures or video of it. This dog is lucky to have neighbors that care so much!
In my area the only time they but a hold on an animal is when it is a stray. I would think that you would have to go through their adoption process, so maybe you should check and see what it is. Some places require you to get preapproval to adopt a pet, maybe you should fill out one of their applications right away if your neighbor does get the dog taken away or signs it over. And let the adoption coorninator know that you already have a history with the dog and would love to adoted it if at all possible! Good luck and keep us posted!