lifetime ~ [M(sun)/m(ion)] x 1.5 x 1.4 x10**(-16) x 10**7 Kelvin / L
lifetime ~ 2 x 10**47 / L seconds
lifetime ~ [ 2 x 10**47 / 4 x 10**30 ] seconds
lifetime ~ 5 x 10**16 seconds ~ 1,700,000,000 years
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.