Most short sale bans no longer exist at the end of trading daily. They are almost like circuit breaker rules where if price moves beyond a certain percentage shorting is not allowed. Your real concerning for checking if a stock is short-able should rest on whether there are shares available to short. Typically if average volume is over 100,000 K and the ipo date was more than three months in the past shares will be available to short for stocks on major exchanges.
So we don't really have a short-able list perse. Its just something the SEC will issue for a given day of trading is movement has exceeded a certain percentage decline.