Today, medical science has proven that all the organs and structure of the human body have the capability of functioning a longer period of time than normal life span of humans. A shorter life is often due to the misuse of one's own body. Even if we assume that this discovery is wrong, it would still be logical that Imam Mahdi (PBUH) live such a long life. This is simply because Allah (SWT) has willed it. He does whatever He wants to do (1), and He is omnipotent. Allah (SWT) is the One who has given existence to mankind and created him from nothing, along with the creation of all the skies and galaxies. Would it be really impossible for Him to protect one from the factors that may cause death? It is remarkable that those factors are creatures and under the control of Allah (SWT) as well.
Moreover history has even shown that there have been many people who lived much longer than Imam Mahdi (PBUH). Prophet Nuh (Noah) (PBUH) for instance lived at least 950 years according to the Holy Quran (2) and 2500 years from other Islamic sources. Also, according to the Holy Quran, Prophet Jesus (PBUH) is still alive.
The absence and occultation of Imam Mahdi (PBUH) does not imply that he does not exist, but it means that people do not recognize him. It has been mentioned in the narrations that Imam Mahdi (PBUH) is like Prophet Yusof (Joseph) (PBUH). He lives amongst them, walks in the streets and bazaars, but people do not identify him.(3) Or in some other narrations he performs the rituals of Hajj, and the people see him but they do not know him.(4)