The government cutting off my payment is one of my biggest fears so I can empathise, it would turn my whole world upside down. The first time I applied for the disability payment I had just started attending a new clinic for therapy, and they rejected me because it was unknown whether that new treatment would magically cure me, when I knew it wouldn't.
I talked about it with my doctor a couple months later and he was very supportive and helped me reapply and that time I got on it, sadly it'll be reviewed in a year which I worry about even now. The interviews are horrible because I'm so bad at explaining my situation.
Good luck with your appeals, perhaps your doctor could write a letter for you? It's also worth finding out more about the whole process, for example here (in Australia) they have very specific rules, something along the lines of:
the condition has to be diagnosed, treated and stabalised,
gets a certain amount of points on an impairment chart,
and is not likely to improve for the next 2 years.
But I don't know if the disability payment here is even comparable to the one they denied you. Also one of the few jobs I've had was at Domino's, I just applied on their site and got a job a week later. I couldn't handle the stress of manning phones and the manager was a wanker, but it was very easy to get.