If you are worried about the health of your frangipani, you should cut off all flowers. Flowers do nothing to improve plant health and strength but use up lots of the plant’s energy. You can also cut off all old leaves so that only small leaves growing from the tips remain.
Before a frangipani die, rot attacks the weak parts of the plant and spreads until the whole plant is dead. you can find how healthy and unhealthy your frangipani is by checking how much rot there is and where the rot is. See the article on checking for rot.