Whatever that takes a form in this world, be it a tree, a human being, a bird, a mountain, etc, has to cease to exist one day.
That is law of the NATURE.
Sages, though enlightened, do follow this Natural law. Swami Vivekananda followed this principle of the Nature.
However, each sage will remain in this world as long as their allocated work has been accomplished. When their allocated work is coming to an end, they choose one way or the other to leave their mortal body.
Sri Ramana Maharshi suffered with Gangrene on his hand, Sri Shirdi Sai suffered with Asthma, and so on.
Disease at the end of accomplishment of their work, will be allowed by the sages, to be a cause for departing from the body.
The last days of Sri Ramakrishna Paramahamsa are to be remembered here.
One day when Narendra was on the ground floor, meditating, the Master
was lying awake in his bed upstairs. In the depths of his meditation
Narendra felt as though a lamp were burning at the back of his head.
Suddenly he lost consciousness. It was the yearned-for, all-effacing
experience of nirvikalpa samadhi, when the embodied soul realizes its
unity with the Absolute. After a very long time he regained partial
consciousness but was unable to find his body. He could see only his
head. "Where is my body?" he cried. The elder Gopal entered the room
and said, "Why, it is here, Naren!" But Narendra could not find it.
Gopal, frightened, ran upstairs to the Master. Sri Ramakrishna only
said: "Let him stay that way for a time. He has worried me long
After another long period Narendra regained full consciousness. Bathed
in peace, he went to the Master, who said: "Now the Mother has shown
you everything. But this revelation will remain under lock and key,
and I shall keep the key. When you have accomplished the Mother's
work you will find the treasure again."
Some days later, Narendra being alone with the Master, Sri Ramakrishna
looked at him and went into samadhi. Narendra felt the penetration of
a subtle force and lost all outer consciousness. Regaining presently
the normal mood, he found the Master weeping.
Sri Ramakrishna said to him: "Today I have given you my all and I am
now only a poor fakir, possessing nothing. By this power you will
do immense good in the world, and not until it is accomplished will
you return." Henceforth the Master lived in the disciple.
So Sri Ramakrishna Paramahamsa told him that he will remain in mortal body, as long as his allocated work is not accomplished.
Swami Vivekananda found his own way to leave the body, after accomplishing his allocated work by the DIVINE.
As I had stated above, disease is only an excuse to leave the body.