Keep in mind that I don't grow this plant and thus have no experience in its care or propagation. To my (old) eyes, I just wouldn't keep butting my head against the wall, trying to salvage such a sick-looking plant. Another thing that concerns me, and this may have been discussed before, is the timing of rooting. Typically, for the plants I am going to air-layer and root cuttings from, I would never do this in the winter. Wait to do it in the spring when the plant comes out of semi-dormancy and when growth begins anew.
Can you air-layer a branch or two and perhaps take a couple of cuttings from another branch or two?
Hopefully, there are those out there that grow/propagate this plant and will know "better" information on what you should do. My suggestions are only based on what I do with the tropical plants I grow and propagate.
