Hi,
The life time of sunspots range from hours to a few months. Sunspots appear at the centers of strong magnetic regions (called Active Regions). The magnetic fields of the Active Regions emerge from below the solar surface. Once their emerging phase complete, the active region magnetic fields spreads and weakens. When the magnetic field is weak enough, the sunspot disappear, although the active region may still be there and later blends in with the quiet Sun.
I am working on an active region now, the sunspot in it lived about two months, but the active region lived for five months.
But since we can only observe one half of the Sun facing earth. The Sun completes one rotation in about one month, a sunspot can only be on our side of the solar disk for maximum two weeks, then it goes to hide on the back side of the sun. So sometimes, one can not be sure whether you are looking at the same sunspot. In fact, NOAA signs a different number to a sunspot each time it appears even it is a returning sunspot.
Hopefully in the future, we can send a satellite that goes around the Sun!
Yan