The process is so convoluted that it'd take the whole article to fully explain it, but, in short, there are four different stages that a claim can go through and four different offices that can review it. Things can go wrong at any time: The vet might be missing one key piece of documentation at any stage, so they get denied. They appeal the decision but still don't have the documentation they need, so they take a lovely boat ride down denial. We lawyers call the process "the hamster wheel."
One client made it to the Court of Appeals for Veterans Claims (the supreme court of veterans' claims) before being chucked back to the regional office and told to start all over again. He looked at me and said, "I just thought I'd file for this and get it. I never thought I'd have to go to war over this."
To win their claim, a veteran needs to prove they have a disability, and they need to prove it came due to their time in service. This often requires a formal medical opinion from a doctor, but you also need to provide every piece of paper ever to do with that case, going back decades. That includes service records, medals awarded, in-service medical treatment records, VA hospital visits, private doctor records, copies of past decisions by the VA, and possibly even detailed disciplinary records from kindergarten just to see if your injury might be related to drinking paste.