Miles’s wife left him because he was not able to age, and she was.
When the Tuck family first drank from the magic water, they did not realize it would make them immortal. As a result, they lived normal lives for a while before realizing they were not aging. His wife could not handle it, and she left. Miles explained that he thought about looking his children up, but it would do more harm than good.
They’d have had a pa close to the same age they was. No, it’d all have been so mixed up and peculiar, it just wouldn’t have worked … (p. 84)
Miles understands why she left. Miles does not stay away out of lack of caring. He is just trying to save himself and his family the pain that it would cause to know that he will never age, and they will.