A tornado keeps going until it becomes detached from the forces that created it. Usually, it's host thunderstorm moves away from the forcing mechanisms that would otherwise keep it operating efficiently.
For example, the storm may outrun or be left behind by the jet streak (a fast-moving ribbon of air embedded in the jetstream above the storm). In this case, the storm would no longer have the suction above it to continue to draw up enough air to keep the tornado vortex alive. The same goes for vorticity (a curving of air above the surface), or a dry middle-layer of air. If its thunderstorm either outruns or otherwise loses these elements, the tornado will begin to weaken and die.
The storm may also move into a cooler, less moist environment, which would rob the tornado of its basic fuel.