According to the FMA:B series, the homunculi aren't supposed to grow old. Moreover, all of the homunculi other than Wrath (King Bradley) could regenerate themselves. This even includes Greed, who's also a human-based homunculus. We also see in the series that during Bradley's death, his body degenerated. If he was able to grow normally then there shouldn't be such things happening to his body.
King Bradley was part human and part homunculus.
He was born human and raised in a facility to train boys to rule. They were injected with philospher stones and, in most cases, died. They could only survive if one strong soul took control of the body. Only Bradley was able to survive the process but it is unclear whether he truely did. A philosopher's stone contains many human souls and not even Bradley knows if the one controlling his body is the same one he started with.
As his body is mostly human, it ages.
It should be noted that the only other known human to survive this is Ling who became Greed. It was clear in that case that both souls remained in Ling's body.