Demon will last up to 30 days on outside surfaces depending on the rain and sun exposure but is not actually labeled for grasshoppers.
Talstar P would be a good choice for grasshopper control and will last up to 30 days as well. You should start applications before the grasshoppers have a chance to hatch for best control. You should thoroughly spray your lawn and water in the application with about a .25 in of water to help the product get past the thatch layer and into the soil where grass hoppers actually develop. If you already have grasshoppers you can use Talstar P at the highest usage rate of 1 oz of product per 1 gallon of water for the quickest knockdown. Use sufficient amounts of water to help the product get to the soil layers.