haberdashers. I thought I knew a good bit about growing plumeria, but this really stumps me. Without your explanation of your care, I would say that freezing temperatures is the reason for what you see. But your plant has not been exposed to freeze. It certainly does not look like it is secondary to over-watering. Cold and over-watering are the two main reasons for rot.
I don't think you will have much success with the tips that are very short, though some say they can root them. I have never had success doing so. I would begin to take cuttings, removing all the sections of stems that don't show white when cut and ooze white "latex" at the cut ends. If there are any stems or base plant that shows black/brown, toss that stem. You want those cut stems to callus well and then try to root them. I would keep the base stem almost dry, only misting every week or so. If it doesn't grow leaves, its a goner.
As a side-note. This doesn't look like a compact grower but you said you have had the plant for 3-4 years. My standard size plants would have grown several feet after that length of time, perhaps growing 2-4x as large as when I first got her. I don't know why yours has not grown. As I say, I am no expert here. I just have a lot of plumeria. You are much closer to being in a sub-tropical climate than I. Most of my plants go through 4-5 months of complete dormancy. I will lose some of the weaker plants during that dormancy but your dormancy is much lighter, much shorter. I just don't know what's going on.
