Naturally, the guy finds a woman in his new time frame, falls in love with her, and, well, you know. Only this woman turned out to be the mother of the man before his time-travel incident. He ultimately has fathered himself and created a severe loop in which the boy's origin (the loops's beginning) has no rational explanation.
Perhaps there was an original father who, the second time through, didn't copulate with the woman because of her actions with the other who wasn't present in the first iteration, but will be for each successive pass of the loop.
Furthermore, let's examine the components of this boy. With the first iteration, he has compostion of 50% his mother's and 50% his own. Once the iteration ends, the boy is fathered by the 50-Mom and 50-boy with a 100%-Mom. This creates a 75%-Mom, 25%-boy Boy. He does the same, and the percentage of his own genetic structure is decreased by half with each pass.
Assuming time runs indefinitely, and we are experiencing an infinite iteration, this individual posesses a genetic structure exactly that of his mother's, the only difference belonging to his gender.
Note that this allows for there to be a young and old version of the same individual to coexist. A Boy Senior and Boy Junior, if you will. Once the moment hits when the boy travels back, all who remains is the one who has already experienced the entire pass and understands where his son went to, whereas his wife, who he has never told, does not.