Don't think they DO that anymore?!! Do what? Appeal on behalf of the customer, have a financial/loan program....
Like I said before, when we first ordered our vest, we were contacted by a rep, who explained the procedure, that usually the first time with our inurance (BCBS), they deny it, then we have to answer more questions, which we did... If it hadn't been approved by them, then there was another appeal process. If that was exhausted then they had their own financial department -- where we could take out a loan to pay off the balance over several years.
I know a family who ended up doing some sort of rental/lease deal. Another who got a loan for the remaining $3,000 that wasn't covered... IMO, ask to speak with a supervisor, get on their website, email, call...
Have you spoken to anyone from your insurance company yet?