When Brand and Cooper return to their ship from Miller's planet, Brand sees the aged Romily and says 'why didn't you sleep?' Later, on Mann's planet, Dr. Mann says he didn't specify an end date the last time he went into cryo-sleep.
Would Dr. Mann have eventually died of old age in cryo-sleep, or would he have stayed the same age? If Romily had been in cryo-sleep for the 23 years that passed (relative to him) would he have stayed the same age as he was when Brand and Cooper returned?
Revived Mann appeared to not having aged at all, even though the same 23 years have passed for him as for Rommily. I believe it's safe to assume that the cryo-sleep does suspend, or at the very least greatly slow down, the aging process in humans. Had Rommily gone into cryo-sleep, he'd probably be just as young as Brand and Cooper.
That is not to say that cryo-sleep would keep a human alive infinitely. The biological processes probably still happen, just much slower. If there was nobody left to revive Mann, he would likely have died from old age eventually. However, it would more likely be because of some technical break-down of his cryo chamber.
I don't think it can make a person immortal. Rather it can elongate the life process.In the end of the film an older Murphy is revived from cryosleep before her death.
When Cooper wakes up, he asks "Is she still alive?". The doctor says "She'll be here in two weeks. She's too old to be transferring from another station, but when she heard you had been found, well, this is Murphy Cooper we're talking about". As Cooper is approaching Murphy's hospital room, the nurse tells him "She's been in cryo-sleep for almost two years." The implication is that as Murphy reached the end of her life, she went into Cryo-sleep so she would still be alive if/when Cooper was found. Now that he has, she's been revived and transferred from the station when she was in cryo-sleep, so she can see Cooper one last time before she died.
