Their roots were probably well on their way to rotting and are unable to sustain the top growth. That is why they die from the top, as that is the farthest the system has to go to carry water, nutrients, etc. and can't reach it because the roots aren't working.

I would think anything less than moist potting soil (albeit well-drained) wouldn't be good for the roses in the summer. You don't want them constantly drying out and having to water twice a day.

I fertilize mine with Osmocote at the beginning of the season, then maybe once monthly with a liquid flower fertilizer.

I've got one big one that's started to do it. I repotted it awhile back. I can't help but think my potting soil is the culprit. It is a local brand called Martin's Potting Soil. You can't get it anymore, but I bought up a bunch three years ago. I always liked it better than any of the other brands.
Mostly because it held water better. Seems to have more nutrients for the plant, too.
Potted roses are one of the trickiest things to grow, I think. You get to wondering what the nurseries do, and what their die-off rate is.

I am planning on growing a potted rose, which I have never done before. Thanks for posting this! Doesn't it help to add extra perlite to the mix?

By typing potting soil for potted roses into Google, several articles come up. Here's one.

Here is a link that might be useful: Potted Roses

The Container forum on GW has an ongoing thread about the best container mix. I suspect yours is too waterlogged causing root rot and no oxygen, the main problem with most container mix.

There is an interconnection between how much you water, how much you fertilize, and potting soil. I don't tend to water a lot, so potting soil that holds water works very well for me. A better-draining soil would probably condemn my roses to death. Somebody who thinks they have to water every day should use a very different soil.

I know it's against the grain to disturb a struggling plant, but since you're seeing consistent symptoms....turn one of these die-back vics out of the pot and take a look and smell.

Use water soluble ferts, double diluted. I don't fertilize struggling plants until they show signs of growth.

Potted roses are easier to grow than roses in the ground from my experience. Really, the only thing you need to watch is that they get enough water and don't dry out like any other plant. I throw Rosetone on my potted roses, but also use half diluted Miracle Gro liquid fertilizer every couple of weeks. The rose will use nutrients quicker in a pot since there is less soil to accomodate all of the roots. If you use liquid fertilizer only, you will just have to dilute it by half to prevent burning and feed more often. For example, if you feed your ground roses full strength fertilizer every 4 weeks, you will have to feed potted roses half strength every 1-2 weeks to keep up with nutrient uptake of the rose as it will deplete the soil of all of it's nutrients.

Just make sure you have good drainage and don't let your potted roses accumulate water at the bottom and cause root rot. As long as the pot has holes in the bottom it should be fine.