i would write a formal letter, outlining the situation and what you expect them to do - it is their responsibilty to keep their dog out of your garden and you will be seeking recompense for every little bit of damage everytime he does it - be it new soil, new flowers, even new cat, should it get hold of one of them.
explain that you should not have to keep returning the animal and fixing the fence and if they still wont deal with it, say you will consider the dog a stray next time and take the dog to the pound ...
i know its harsh and im not saying do that, but letting them know you mean it and that not fixing it could cause more issues may make then sort it out
you could also, assist them by printing out relevant products etc such as deterrents, electrical and chemical, and types of fencing, to show them what you are expecting of them.