Has it formed any roots in the water at the bottom? Sometimes a rose will sprout new growth on the canes using the energy it has stored in the cane but without roots it can't maintain it. If you'd like to try and root it I would place it in a clear plastic cup filled with potting soil. Punch a hole in the bottom of the cup so that it drains well. If the soil is too moist the cane may rot. Before planting it in the soil scrape the sides of the cane and expose the white inner layer of the cane. Dip it in some type of rooting hormone. Poke a hole in the potting soil with a pencil and place the cane in the hole. Firm the soil well around the cane and put it in the light. Keep it well watered but not soggy wet. It should take 3 or 4 weeks for it to root. The plastic cup allows you to see the roots through the cup so you will know when it's rooted well. If the cane turns brown or black, unfortunately, that means it's died. Good Luck!