One of my sons is an Astronautical Engineer at NASA. His first mission was flight operations on a solar observation satellite. Some years before, an on-board gyroscope broke and the spacecraft turned away from earth. They set up a program to call out in case it ever righted itself. A couple years later, it did and they were back in business.
The satellite first went live the year he was born and was supposed to be operational for 2-3 years. He began working on that mission as a college student and the satellite was still operating.
That's the usual arrangement. The mission is FINANCIALLY authorized for 2-3 years. The spacecraft is designed and built to operate for five to ten times that long. There are periodic program reviews to assess the spacecraft's condition and authorize extensions of the mission if warranted.
It is amazing how sometimes (often?) NASA gets things right. Like the Voyagers and the Mars rovers. Keep going and going.
BTW - even though Voyager 1 is farther than Voyager 2, Voyager 2 was launched first! (I forget the story behind that). Voyager 2 took the detour to Neptune and Uranus, while Voyager 1 took a faster, more direct route. Voyager 1 is still traveling faster than Voyager 2.