I don't believe the roses themselves would leave any residue that should affect the soil negatively. However, if you were doing some of the heavy duty applications (i.e. lots of high P bloom booster fertilizer or soil drenchs of pesticides that rose exhibitors sometimes do) that could have some negative affects on your soil. If you were just applying fertilizer & mulch like you would to a normal shrub planting, should be no problem. I would do a soil test to see if you have a pH or nutrient problem. Also is there some large tree with invasive roots nearby? They love to invade a rose bed that has been watered & mulched.

What did you plant, when did you plant, what are you doing maintenance-wise? Are there large trees close to the area? If so, what kind?

We've had drought conditions for a couple of years, making it tough for new plants.

Those factors are more important than what was planted there before.

I planted a variety of evergreen plants, both shrubs and groundcover types. These areas receive regular watering. I wouldn't be posting here if the problems were ordinary. They are not. I have noticed situations that I would not expect as a fairly experienced gardener. That is why I have posted here.

It is perfectly possible for fungal problems such as a verticillium wilt...or armeria....to cause growth problems. In the UK, land which has been used for growing roses is not suitable for growing other roses - Rose Replant Syndrome....or rose sickness......but this tends to only affect roses and close relatives in the rosaceae family.
A bit more information would be helpful - how are they dying? All of the plant? parts of the plant? Do they change, looking dry and shrivelled, say? Do they just fail to thrive? And pictures would be really useful, if you can.