"Hail and Farewell" by Ray Bradbury.
But of course he was going away, there was nothing else to do, the time was up, the clock had run out, and he was going very far away indeed. His suitcase was packed, his shoes were shined, his hair was brushed, he had expressly washed behind his ears, and it remained only for him to go down the stairs, out the front door, and up the street to the small-town station where the train would make a stop for him alone. Then Fox Hill, Illinois, would be left far off in his past. And he would go on, perhaps to Iowa, perhaps to Kansas, perhaps even to California; a small boy twelve years old with a birth certificate in his valise to show he had been born forty-three years ago.
'Willie!' called a voice downstairs.
'Yes!' He hoisted his suitcase. In his bureau mirror he saw a face made of June dandelions and July apples and warm summer-morning milk. There, as always, was his look of the angel and the innocent, which might never, in the years of his life, change.
'Almost time,' called the woman's voice.
'All right!' And he went down the stairs, grunting and smiling. In the living-room sat Anna and Steve, their clothes painfully neat.
'Here I am!' cried Willie in the parlor door.
Anna looked like she was going to cry. 'Oh, good Lord, you can't really be leaving us, can you, Willie?'
'People are beginning to talk,' said Willie quietly. I've been here three years now. But when people begin to talk, I know it's time to put on my shoes and buy a railway ticket.'
What was I? A boy. I looked like a boy, sounded like a boy, so I might as well go on being a boy. No use fighting it. No use screaming. So what could I do? What job was handy? And then one day I saw this man in a restaurant looking at another man’s pictures of his children. “Sure wish I had kids,” he said. “Sure wish I had kids.’ He kept shaking his head. And me sitting a few seats away from him, a hamburger in my hands. I sat there, frozen. At that very instant I knew what my job would be for all the rest of my life.