He's probably not doing well because he cannot swim properly, but that doesn't necessarily mean he'll die. One of my male flag cichlids attacked his mate while I was out one day, and when I came home she was laying on the bottom of the tank with no fins. I put her in a bare-bottom hospital tank and kept the water really clean. She laid on the bottom for a few days, but eventually managed to hold herself upright and eat. After a month or so she was completely healed and she is still in my community tank.
Melafix works for some, but I'm a firm believer in clean water. I don't dump chemicals in my tank unless it's absolutely necessary. As long as the tank and water are clean, it should heal whether you add Melafix or not. JMO.