lifetime ~ 10,000,000 [M/M(sun)]0.6 [L/L(sun)]-0.6 years ====> 1,000,000,000 years for a 0.001 L(Sun), 1 M(Sun) white dwarf.
For less luminous white dwarfs, the lifetimes can be as large as 10 billion years and white dwarfs can also serve to place a lower limit on the age of our Galaxy (and hence the Universe).
The key point of the above is that the lifetime of a white dwarf is long. Further, they only stop being white dwarfs because we arbitrarily say that they are not white dwarfs once they become cold and faint.