Sorry to say that that looks dead. If you are purchasing bagged bare root roses at this time of year chances are most of them are already too far gone when you get them to make it. Those roses were harvested last fall. They were dug up, stripped of all their leaves, soil and a lot of their roots and chopped off top and bottom to fit in those bags. Then they were placed in cold storage all winter to go to the stores in February and March. Now they've been sitting on a store shelf since then with no care or water of any kind. The store is cutting the prices to get rid of them, and that's appealing, but they really aren't worth the money. If you have a good nursery near you I'd suggest you go pick out a nice potted rose that's already growing and healthy and start with that.

I think you are right. The ones kept dying are the replacements I bought from late April to June, and the first batch I bought in early March are fine. Thanks for the useful information!