Everybody is mortal. How can he live so long?
Yes, in fact Imam Mahdi will die too. But the difference is the length of life in this world. In fact, Quran and the prophetic traditions tell us that some people have had/are having long life in this world. So it is possible to see this phenomena again.
Are you aware that according to the Quran (see 29:14), Prophet Noah has just been prophet for 950 years? In fact, he was alive even more than that because we should add his age before prophethood to the above number. Who knows how much it was.
Do you agree that Prophet Jesus (AS) is still alive? He is in fact 1,994 years old now. Of course, he is not living on Earth right now; he is living in the Heavens. But according to Muslim's belief, he will come back to Earth, and will pray behind Imam al-Mahdi (AS).
Do you agree that al-Khidr (AS) is still alive? Quran mentions his story with Moses (AS). He existed before the birth of the Prophet Moses (AS), so al-Khidr (AS) is now more than 3000 years old. He lives right here on this Earth, but we cannot recognize him (fairly similar to the case of Imam Mahdi). He serves Allah (SWT) as one of His agents.
No doubt Allah has the ability to give a very long life, but He also has assigned a death time for everybody (including the above mentioned individuals) which can be so soon or so late.
Moreover, scientifically speaking, there are NO objections whatsoever to the extended life span assertion. A group of scientists conducted a series of experiments at the Rockefeller Institute in New York in 1912 on certain "parts" of plants, animals, and humans. These scientists included Dr. Alex Carl, Dr. Jack Lope, and Dr. Warren Lewis and his wife, among others. Among the experiments conducted was one that directly treated the nerves, muscles, hearts, skin, and kidneys of human beings. These organs were not in a human body, they were independent organs that were perhaps donated for the experiment. It was concluded by the scientists that these "parts or organs" CAN continue to live almost indefinitely as long as they are nourished properly, and as long as they are shielded from external negative interactions like microbes and other obstacles that might inhibit the growth of these organs; furthermore, the assertion was made that the cells would continue to grow normally under the above conditions, and that the growth is directly related to the nourishment provided. Again, aging had no effect on these organs, and they grew every year without any signs of deterioration or aging. The scientists concluded that these organs will continue to grow as long as the patience of the scientists themselves is not exhausted, causing them to abandon the nourishment process.
Source: AL-SHIA.ORG