Why does Ralph feel that his indefinable connection between himself and Jack mean that Jack will never stop searching for him?

Ralph and Jack have become bitter rivals on the island. As a head choirboy, Jack is used to leading others, so he is rather put out when Ralph initially assumes leadership over the boys. This sets in motion a series of increasingly disturbing events in which Jack becomes more savage and unhinged. Destroying Ralph becomes almost an obsession for Jack. So long as Ralph lives, he will always represent a serious threat to Jack's power and authority, and Jack simply cannot, and will not, allow that threat to go unchallenged.
Jack has become obsessed with blood and power in fairly equal measure. This is a toxic combination indeed. They say that absolute power corrupts absolutely, and that is certainly the case here. Jack will be damned if he is going to give up his power to Ralph or anyone else. That is why he will never let Ralph be; that is also why, so long as Ralph lives, Jack will never stop searching for him.