Children often will start questioning their environment and those in it when they are five years of age or so. This is because preschoolers tend to be more egocentric and elementary aged children are just learning to be aware of social situations and events.
I recently heard Wendy Young, LSW discuss children and grief on the interview available here: http://ht.ly/1G6bO
She also has written a very good book to understand this topic and help your children with these questions and/ or grief. The book, if you wish to peruse, is available here: http://www.kidlutions.com/griefworks.html
Good luck and I hope this information helps you.
Louise Masin Sattler, NCSP
Nationally Certified School Psychologist
Owner of Signing Families
Host on HerInsight media - Learning and Laughter with Louise (www.toginet.com)
This can be very normal. This child may have just made the developmental discovery wherein he/she now realizes that death is real, it is forever and that it happens to everyone. Therefore, the child may realize that he/she will someday die, too. (I would wonder if there was a recent death of a close loved one for this child. This could certainly contribute to the fears.)
The best approach to this is to tell the truth, which is that every living thing dies. HOWEVER, most people die when they are very, very, very, very, very, very old. We have very good medical care that can help us alive for a very long time.
If this is explained in a developmental appropriate manner and the child continues to have a great amount of fear over an extended period of time, then there may be underlying anxiety issues that can respond well to treatment. If anxiety is found to be an issue, the earlier it is treated, the better outcomes the child may have.
(Thanks, Louise, for sharing the other links from the interview on dealing with grieving children, as well as my workbook information. Thanks, also, for translating some of the interview into American Sign Language.)