Green Cabomba!!!
First you need to take them out and plant each stem individually with the leaves almost but not quite touching the leaves of the stems around it. his allows light and water flow to reach the bottom of the stems and leaves. TCabomba can be picky but have found using liquid carbon such as Excel helps alot. Also they like alot of nutrients and I strongly suggest using at least something like Seachems Flourish Comprehensive once or twice weekly along with API Leaf Zone to add potassium and iron to the water also. What type lighting do you have? They like at least medium light.
Falls apart easily?
I'd actually just cut the rings off, trim the stems to just below the leaves and replant individually. Check out the first full tank picture on this link, look at the green stem plant in the back and slightly to the right. See how you can see each individual stem planted next to each other and their leaves are almost or just barely touching the other stems leaves? This is what I mean... Art of Aquascaping: Which Style Fits You? | AquaScapist.
I don't have any leaf loss issue in the tank I have it in and I use liquid carbon. I have the Cabomba Furcata and like it so much I have two groups of it now.
You actually do just stick the stems down in the substrate. Stem plants take nutrients almost exclusively from the water but they do develop weak root systems just to anchor themselves. If your afraid of them floating just push them deeply into the substrate. It really is as simple as that.