Can you show us a picture of it? I'm not sure if you're talking about a Pedilanthus or something else.

Here. You can see the empty nodes where the curled up dry looking leaves dropped off. I think this is Euphorbia tithymaloides 'Variegatus'. I'd love to know how to get a bushier plant, and why the leaves drop off if I don't water it like every other day.

just a thought: poinsettia is also Euphorbia and if allowed to dry completely also will drop leaves. just barely moist is what it likes. I read the same about Euphorbia tithymaloides. Although when in ground it behaves more like a real succulent and can tolerate dryness. It is a native FL plant and grows in dry tropical forests in central America. so very hot and high humidity too.

I've seen it growing outside in central FL in great thickets in dappled shade.

if you give it good hot sunny window you can probably water it more.

that said...Poinsettias drop leaves when too wet too - so..a lot depends on how water retentive your soil mix is.

I can easily keep Poinsettia going in self-watering pot, but with half perlite for aeration. I also grow other succulents like Jades and Sansevieria and hawortias on top wicks (wicks inserted around the perimeter of the pot to wick less, as opposed to bottom wicks). my jades drop very few leaves when grown like that. when I don't wick and allow them to get bone dry, that's when they drop most..

so you need to observe and experiment a bit and water very carefully only when at least half the pot is dry.

what sort of mix is it in?

I'd guess that the soil that it's in is the cause - it should be a porous mix, with room for the plant to grow. Perhaps the plant's rootbound?

I think I used a soil especially for succulents and cacti.

That, unfortunately, might be the problem - all C&S soils aren't created equally. BTW, lower leaves drop off, as the plant grows and new leaves are produced.