Tenant question regarding fence and dogs?

You need to speak to your landlord about it, you should have already. Doent the damage and what you do to fix it. Your landlord has a responsability to you as his tenant to care of problems. However, the neighbor is at fault and they have a responsability to your landlord as the homeowner. Sounds to me like your landlord needs to know what is going on so he can approach the neighbors. If they are cooperative then they can deal with it directly, but if not, then he may have to sue them for damage and report the dogs to the animal protection society in your area.