May I offer up my 2cents as well here? Recently my Dom had a major health scare and I was very worried I would lose Him. So I can understand what your sub is going through. Nothing is worse than thinking you might not have that one person who you have come to depend on for your safety, love, support, and so much that is hard to put into words.
From my experience it is not only the fear that you may get sick while she is bound and helpless to assist you. But, also that she may have a hard time getting into a scene....letting go and allowing you control. I was so watchful every moment with my Dom that I couldn't be fully present and enjoy. His illness required a break from playing, and the first time we tried bondage again after I was physically uncomfortable, not just in the ropes, but within my skin and in my mind. It's hard to describe the fear...I trust Him completely, but I was so scared that I might drop my guard and then something terrible would happen. We stopped that night and spent a long time talking.
All I have found that works is time and slowly rebuilding my faith that I can let go and nothing bad will happen. We had playtime without any bondage, then used Master's will techniques where I was bound by his command alone, and only recently broke out the cuffs and ropes again. The first time I allowed myself to hit subspace again was a major moment, and then seeing that nothing bad happened while I was out of it reinforced everything He had been saying about being fine.
I also wonder if the way your downplay the significance of death, and don't fear it as you say, is contributing to her increased worry. Almost as if she can't trust that when you say nothing is wrong, you are indeed 100%. I needed my Dom to stop trying to be superman for me, and admit to me when He didn't feel well, even if it was "I'm really tired tonight, I think I'm going to go to bed early." Hearing him take care of his physical well being, and not try to hide it if he was doing so great one, allowed me to trust that He was taking care of himself.
Another suggestion: maybe she find a support group for people who have dealt with serious illness in their loved ones. I went to a few meetings, learned how to deal with my fears, heard from people who had gone through similar situations and how they got back to normal. It probably isn't just in the bedroom that she is afraid....so learning how to accept those fears and work past them might help in all areas of your life.
Ok sorry that rambled a bit....much more than 2 cents.... it was selfishly good for me to able to put my own experiences out there. Good luck to both of you. With time and oodles of communication I'm sure everything will work out well. Also, if she ever wants to talk to me she is welcome to message me anytime. Sometimes just voicing your fears to someone else is helpful.