Some roses have naturally floppy canes.

Immature roses might have weak canes, as the rose matures it builds up a structure and the canes can strengthen.

What type of rose is it, and how old is it?

If you have pics of it, that could help to diagnose what might be happening with it...

Hi Centifolia: you are correct that alkaline soil make rose canes weak. I have alkaline soil high in limestone (calcium). If you google, "Recognizing Nutrient Deficiency Symptoms", it will pop up a site by James W. Boodley, Professor at Cornell, New York. It says, "high calcium levels induce potassium deficiency."

Potassium is needed for strong stems. I also hard water high in calcium. My roses give weak stem, smaller flowers when I water them with my alkaline water, pH of 8.

In the spring I don't water my roses with the rain here. Rain water is acidic, pH of 5.7 - the roses have big stems, bigger blooms and dark green leaves in the spring.

Sulphate of potash is recommended to solve potassium deficiency. Symptoms are: weak stems, marginal scorch on the lower leaves, azaleas turn red ... I see blueberry plants at Walmart turn bronzy red when watered with alkaline water.