Dear T,
Acute onset separation anxiety is not too uncommon in three-year-olds. If the child's day-to-day life is stable, without chaos or major changes or losses, it's best dealt with by patience, support and understading, with reassurance. It's not a good idea to let the child's fears drive the family's activity. For example, let's say the parents plan to go out, the child voices worries, and the parents respond by cancelling their plans. That would not be good. The parents should be supportive and encouraging, all the while going about their planned activity.
Now, sometimes such separation anxiety appears in the wake of troubling events, changes, trauma, losses, etc. the child is experiencing, and the behavior is symptomatic of their upset. When this is the csae, re-establishing stability and routine is the major need in order to promote the child's sense of security.
This is yet another behavior problems we have had with our 5 yr old son during the last year and a half. My father died in 1998 and took my son to the funeral and burial. Big mistake!! He had really bad problems realizing that his mom and dad were going to die some day and he had the fear that we would die soon and he would be all alone with no one to take care of him.
For months I had to keep reinforcing that we were still young and would not die until he was grown up. Plus we reinforced that that is the cycle of life, you are born, grow up, have children, grow old, then die. Then he will have children and the cycle keeps on going. Then I reinforced that we had made arrangements (in our will) that either his grandparents or my brother and his wife would take him if something happened to me and his dad. I think the fact that he knew what was going to happen to him if we both died and that he would not be alone helped more than anything.
You want to know the kicker? For some reason when we saw "Dinosaurs" he finally got it about being born, growing up, having children, and then the children have children. Since then (three weeks ago) he has not mentioned death nor gotten upset about death.
Plus if you are a churchgoer you can accent the positve aspects of your religion and that you do not have to fear death. Our son also goes to a private Christian school so they helped reinforce the positive side of dying a believer. So now he is pretty Ok about dying, except he wants to take his toys and movies with him LOL!!