I believe that the mystery why Ash remains 10 and why he does not have a father are connected.
Obviously Delia Ketchum wanted to have her son youthful forever, so she created a magic potion that stole years away from someone to give another youth. When Ash was young, she abducted his father and trapped him in a cage in the basement. She decided that she would begin using the potion when he was nine because then he wouldn't have to leave her and he would be the perfect age.
But then Ash's dad began fighting back.
He believed that if Ash turned 10 and left home, Delia would let him (the father) go free and have no use for him anymore. He convinced her to delay her potion until the night before Ash turned 10, to keep him in a the happiest state of his life. She agreed. What she didn't know was that Ash's dad had befriended a Pichu.
On the night of Ash's tenth birthday, Delia Ketchum prepared his dinner and slipped the potion into Ash's chicken. What she didn't know was that the Pichu had swapped the potion with a bottle of water. Ash ate normally and woke up 10 the next morning and the rest is history.
But there's more. Delia, infuriated by her loss, cursed all Pichu never to be wild in Kanto, so they fled to Johto. Not wanting to be beaten, she slipped Ash some of the potion as he left home. Unfortunately for her, he was 10 and was legally an adult, but he was still young. So every year she would slip Ash a potion that kept him 10 years old for another year, making Ash's father a year older in the process. Occasionally she would slip it to Ash's friends, because she didn't want her son to be lonely, and it made her cooking very tasty.
To this day, Ash remains 10 and his father accelerates towards old age at an increasing rate. When he dies, only time will tell who her next victim is.
And yes, this began as an answer to another topic, but it spiraled out of hand...