Whoops! Forget what was said in my last post, then.
Okay, this is a sucky situation for you, JC. Sorry to hear about the horrible *owners* of the house next door.
From what I understand about fence laws (had to deal with a messy fence issue before), they are obligated to share costs of fence repair, but getting them to do it is another issue. I would still try to send a certified letter stating what was said before, but maybe change the wording to: “If we don’t hear from you before xx/xx/xxxx (date), it will be assumed that you agree to the fence repairs.”
Document, document, document…take pictures, videos, etc. of the existing fence. Maybe send another letter just before you take action to fix the fence, and send all letters and photos to the owner and the management company.
I am not a lawyer, and this is just personal opinion based on an experience with uncooperative neighbors, so if anyone else here knows more about fence laws and how to handle this, please chime it.