Arlene, another thing to try is to put them in warm water instead of cold, then take it indoors and let it cool off slowly. You want the stems to keep taking up water. It's possible that the shock of going from your warm garden to the cold water and into the fridge is making it stop drinking. If you want the cut stems to stay alive and perky, you don't really need to make them think it's suddenly winter. I do this with basil, and it keeps on the counter in a glass of water at room temp for a week if I don't use it up.
Also take the container of warm water into the garden with you, and put the stems in it right away. The cut stems can suck up air bubbles if you don't get them into water, which then blocks the uptake of water and causes the tops to wilt.
Roses respond better if you put them immediately into warm water rather than cold, too.