I don't think the real issue is that "born again Christians fear death." In regard to fear, I don't think think any born again Christian necessarily fears death. I think that as humans it is easy to fear things surrounding death.
For example, leaving your family or children behind. When I think of my Dad and his passing away, one of the last things he said, was "Praise God, all of my children are going to be with me in Paradise." The point is, had he not discovered this before his death, it might have been something tough to face in the end. I personally think that it was the hand of God that made Dad believe that. I am not certain that my brother is there yet, but like my Dad, I believe before he dies, God will change his heart and he'll become his child.
My husband worries about leaving me with a ton of bills. Or leaving our daughters without a dad. Anyway, I do not think born again Christians fear death, instead they worry about the things they shouldn't. I believe that God has not only my day planned, but everything else as well, including the care of my children and my husband. I think it is harder for my husband because he is the bread winner. But even though he worries about these things, doesn't mean he is not a Christian or that he fears death. Quite the opposite. He is a Christian, but as we all struggle with something...his is worry.