@Jim Mac that direct sun and heat is literally cooking your rose's roots. Roses can withstand the heat and direct sun, but their roots can't. Sun shining directly on the pot heats up the soil ball and can actually cook the roots which grow out to the pot sides then circle the soil ball as they grow. That heat not only bakes out all of the soil moisture but also speeds up bacterial and fungal activity which digests the organic material in the soil mix faster. It can also incredibly speed up the break down and release of any time released fertilizers you may use. Increasing the heat in the root zone causes water stress on the rose. You can literally force a rose to both rust and mildew by water stressing it. If the roots were planted in the ground, they would remain a relatively constant temperature instead of experiencing the wide swings of cooler night temps to high extremes due to the hot air (like a convection oven) and direct sun (like a gas or electric burner on a pot or pan) on and surrounding the pot.

Ideally, if you can't plant the rose IN the ground, you should use an insulated pot such as a foam, wood or concrete which help reduce the amount of temperature transmitted through the pot sides into the soil ball and roots. You can also obtain a larger pot than the one the rose is planted in, place the planted pot inside it and either use thin Styrofoam or bubble wrap (preferably with as large "bubbles" as possible to maximize the air insulation between the pots) to insulate the root ball against temperature extremes.

Placing the pot ON a hard scape surface increases the heat in the air surrounding the plant very much like putting it inside a convection oven. To get a good idea of the effects of the sun shining on the hard scape, stand barefoot on that hard scape after the sun has been shining on it a while. Try it again a while after the sun has moved from shining directly on it to see how long it continues to radiate that increased heat. The combination of all of these factors literally cooks the potted rose sitting on the patio. That cooking inhibits the rose's immune system, forcing it to try to survive while suffering from fungal (and likely insect) attacks in its weakened state. It doesn't need chemical intervention, it needs heat reduction to the root ball and heat reduction to the air surrounding it to reduce it's water stress and literally being "baked".

You can also reduce the root heat stress by using the largest available pot you can find that's insulated (foam, wood, etc.) or obtaining the large pot and then lining the interior with multiple layers of either Styro Foam or bubble wrap to create the effects of an ice chest and reduce the heat transfer to the roots, then planting the rose inside the insulated container. Larger soil balls insulate significantly better than smaller ones. Of course you have to balance being able to move the plant to winter protect it and heat protection so whichever method of reducing the heat extremes to the roots works best for you to be able to handle the plant is what you should choose. It very likely doesn't matter what rose you select to grow there as those issues will remain if no changes are made. Some may be more diseased due to less genetic immunity to diseases. It's rather remarkable the plant is producing any flowers as flowering is ovulation in preparation to set seed (pregnancy) to perpetuate the species. Enduring those heat extremes could easily prevent it from flowering at all as it struggles to simply survive being cooked. I hope this helps provide you what you need to mitigate the temperature issues the plant is suffering. Good luck!