Somebody needs to attach images of this. I suspect that it is not a problem at all but, as Jean says, aerial root initials. A picture would solve the mystery in a nanosecond.

Maybe it has spider mites? Does the foliage look kind of mottled light gray along the ribs? A photo would help.

Below text was extracted from other link, i hope it will help you. The most common cause of frangipanis dying is by rot. If a potted frangipani plant is watered too much or too often (especially in cooler weather), the soil will remain wet and the stem may start to rot at the base. This known as "wet feet". The rot will travel up the stem and probably end up killing the whole plant. Sometimes rot can start on a branch. Rot can be found in a stem or branch by noticing that it is more wrinkled, soft or black inside. Softness can be checked by squeezing the branch. Piercing a branch or stem will show if the inside contains sap. If the plant is healthy the white liquid will start to flow out and the cut will heal naturally, similar to when an animal or person has a cut and the blood clots.if the stem becomes wrinkled the tree is not well ¡V cease watering and spray leaves with AntiRot. If you notice spongy stems, remove the stem completely to the junction with a main branch. Thinning out 15 to 20 per cent of the canopy of your mature frangipani is good to do every few years; it opens up the branches, allows light in and reduces stem rot.

One point against Native Frangipani is they are brittle and easily wind damaged. Only last weekend I had to remove 2 trees because the wind completly removed the branches from one side of the tree and the second tree split down the middle. This is fairly common with rainforest trees as they are generally shallow rooted and do require the rest of the forest for protection. I have also found too much mulch stops the tree from sending its roots down, The roots stay just under the surface where all the nutrients are. Plant them in a protected position and they should be OK. If planted in the shade the tree will be tall and straggley because it is trying to get to the sun as most rainforest trees have their canopies in the sun. If you plant rainforest trees in full sun they tend to be bushier and only grow to about 1/3 to 1/2 the stated forest height. A good example of this is the Flindersia brayleyana or Qld Maple. In the forest it may reach 40 metres but in full sun only 8 to 10 metres.