@XxxARTSxxX
He is not immortal at all. He clearly ages and still has to survive each day to wish himself back into the locker.
As to why doesn't he wish himself to be younger: There might be a discontinuity of conciousness whenever he wishes himself into the locker. At least that's how I interpret his final thoughts "Is tomorrow me still me?". He is worried what might happen if the "Me" he wishes back is still his true self or if the locker changes something in him.
If he were to wish himself younger, the locker might not carry over any memories and experiences of his current self over, or it might spawn something that he wishes his younger self to be. His current self might not even disappear in this case, but he might just clone himself.
There are similar theories as to what e.g. 'beaming' in Sci-Fi might do to a humans conciousness and 'self' and plenty of philosophical discussions and reading material on what the actual 'self' is.