Since I am not an authority on the issues surrounding unemployment compensation, I can only offer my personal opinion. In other words, my best guess is that the chances of "reinstatement of unemployment compensation or winning an appeal after reporting a job refusal due to a low salary offer, not commesurate with the position and years of experience" are slim to none.
I say this for two reasons, the first being the obvious that because of the current economic and unemployment conditions in the US, few can expect to return to work at a level they had before being laid off. The second reason is that not much of anything has been done to assist those that have exhausted their unemployment benefits and are still without work of any kind.
Nonetheless, a low salary offer should provide a way to leverage other factors in hopes of strengthening a position for an appeal. With gas prices the way they, maybe the salary was so low one couldn't afford the gas to drive to work! Well, we know that won't work. "They" would just tell us to walk to work.