Mark,
How big is your plumeria? How often do you water it, and is it in the ground? Are the limbs and trunk firm or soft?
The drooping limbs sounds serious. My plumeria are
growing in pots because I have to bring them in every winter. If they are healthy, they are very hard due to the milk inside. I've killed my share of plumeria, and if they rot or dehydrate they become soft and mushy and eventually like paper. Plumeria are
succulents. They don't need a lot of water. They need heat and light, and it sounds like you have plenty of those.
