If the owners have not responded to your letters, they probably won’t respond to any future attempts. Send then a letter and have them at least sign off on the repairs or replacement of existing fence at your expense. If they don’t sign the letter allowing you to do repairs, then build a new fence on your side of the existing fence. You don’t want to have any future law suits and this should take care of that. Fence issues are a pain in the butt. My recomendation is to avoid any potential problems and if you want the new fence, you pay for it. Remember you are the one with the dog and potential hazard. I’ve been on both sides of the fence problem and there is no easy solution if one side is not ready to move forward.