Jim is a central character in the show. He does not die or meet any serious harm. He is a young boy throughout the series and grows up as the show progresses.
He experiences some scary moments due to his mother's abilities, but he is always safe and well. He is a source of strength and support for Melinda, and their relationship is a heartwarming part of the show.
Perhaps you were thinking of another character from the show, or you might be remembering a specific episode where something scary happened to Jim. If you can recall any specific details, I may be able to help you recall what happened.