With the exception of the British pound Sterling, no fiat currency has lasted longer than 42 years. In America, we are in year 41.
The average life expectancy for a fiat currency is 27 years, with the shortest life span being one month. Founded in 1694, the British pound Sterling is the oldest fiat currency in existence. At a ripe old age of 317 years it must be considered a highly successful fiat currency. However, success is relative. The British pound was defined as 12 ounces of silver, so it's worth less than 1/200 or 0.5% of its original value. In other words, the most successful long standing currency in existence has lost 99.5% of its value.
Given the undeniable track record of currencies, it is clear that on a long enough timeline the survival rate of all fiat currencies drops to zero.