How much financial wealth is needed to feel secure?

During a gathering of professionals engaged in family business adivising in Chicago earlier this year a survey of ultra high net worth families was mentioned that queried "how much money would you need to have to feel completely secure?" The answer, regardless of wealth level (starting at $10 million and going up to $1 billion) was approximately 80% more than they currently possessed. The book citing the survey was "Richistan: A Journey Through the American Wealth Boom and the Lives of the New Rich" written by Robert H. Frank (the wealth reporter for the Wall Street Journal) and published in 2007.

I was struck by the nearly constant factor at each wealth point: families with a net worth of $10 million would feel completely secure if only they had $18 million; families with a net worth of $100 million would feel completely safe if only they had $180 million, etc. It was as though at each level of financial wealth a family established its lifestyle at the same relative threshold of insecurity. I have personally worked with clients who expressed fear of impending impoverishment, even though they had financial resources in excess of $100 million. My first encounter with a client presenting this fear pattern was with a woman who's family had been wiped out in the Great Depression in the U.S. during the 1930s. I remember wondering if those traumatic memories were the primary reason for what I perceived as an irrational fear since the woman had amassed what most would consider a great fortune. Based on the results of the survey mentioned in the book perhaps there is much more to the story. What experiences have you had that illustrate the "insecurity gap" in wealthy families?