She was damaged goods, because of her harsh childhood upbringing dealing with her father, being with some abusive boyfriends and experimenting with drugs. It's not an unfamiliar tale. Forrest isn't able to pick up on some of these things that the audience does. In his simple mind, she is perfect, but in reality, she's kind of broken.

She always taught Forrest to run when he had a problem. So when she felt she had a problem she only knew how to run away too. It's kinda like this film is about running away from your problems until it catches up to you.

@tmdb43737777 said:

It seemed like she kind of had her life back on track at that point.

Why take off like that?

She had his child, I would think she would want him to know that and he certainly could've helped financially.

Can't imagine she could make enough money to raise little Forest.

One possible explanation is that Jenny was not ready for a committed relationship at that time. Throughout the movie, it is implied that Jenny had a difficult childhood and struggled with personal demons such as drug addiction and abusive relationships. It is possible that she felt overwhelmed by her feelings for Forrest and the idea of settling down, leading her to leave without an explanation.

Her character is very traumatized, her leaving is sad but realistic. Self sabotage…she wouldn’t feel good enough to stay and be happy. Always the urge to run away and be traumatized again…seeking an abuser even.