My leaves are turning brown...is my plant dying?
The plant is absolutely not healthy. There are a number of causes for that type of die back..poor drainage or overwatering which leads to a type of root rot bacteria, also damage to the trunk can allow bacterial infections. I would take the plant out of the pot and inspect the roots for rot and dieback and also for fungal growth or pests.
You can also contact your local Agriculture Extension service for info and help to treat the problem.