D.K.
I think this could possibly be a by-product of our "fear" culture. My suggestion...unplug the TV/video games etc... Get him out and about, doing things. Confront his fears by taking him to volunteer at a children's cancer ward or something like that. Meeting real life children that are facing and fighting his fear will make it seem more vincible to him is my guess. It will show him that health problems don't always mean you have to die. There are many options available to people that get sick and many of them recover to lead perfectly normal lives. Helping other children to not be afraid of this will also have the effect of making him less afraid of it. They say the teacher learns more than the student, so let him be the teacher of NOT fearing death.
On a more personal note, I faced this with my son, who is also 7, but to a lesser degree and it was a couple of years ago. I don't know how religious you are, but religion makes a very convenient forum to discuss this and many other issues with children. This is how I handled it:
The way I explained it to him is that we were put on this earth to live good, full lives and to add value to other lives where we can. When the time we were given is over, then it is our turn to go to Heaven which is paradise and peace. I told him that transitioning from life to after-life is not something to fear, it is a wonderous part of the lives our souls are entitled to by God and it is His right to decide how much time we are given. The important thing for us to remember is that we should be living our lives to the fullest while we are on Earth and fear of the transition at the end of our lives will only get in our way of living the best we can. I encouraged my son to think about it as much as he needed to and to ask me any more questions he might have. I told him all of this with as gentle a smile on my face as possible and a demeanor of quiet excitement about what might be awaiting me on the other side when God calls me home one day. Occasionally he brings it up again, but not out of fear anymore, now it is simply curiosity. Sometimes we review the Easter story which illustrates our belief that souls ascend to Heaven after death. This really seems to help get my point across.
Anyways, this is what worked for me, maybe it'll work for you, or maybe it's not your style, but still hopefully you can find something useful in it. :)