The term immortal really is a misnomer. Although they are called immortals because they live for very long (in some cases, 10,000’s of years), they eventually die.
In Buddhism, all that is conditioned is impermanent. For example, our physical body is conditioned and will, therefore, eventually decay and disintegrate.
The Taoist Dharma is wonderful, in that they cleanse their bodies quite efficaciously, thus managing to extend life. But, that is also a drawback; they are still attached to life. It is that attachment that actually obstructs ever-lasting life. Arhats (or higher level practitioners) manage to drop all attachments, thus ending involuntary birth and death – they can live as long as they wish.