As the core and mantle of the earth cools, it will reach a point where new crust cannot be produced.
How can this point be calculated?
If we can, has anyone done such calculations?
One permanent threat to plate tectonics is the oceans vanishing. The scientific jury may still be out on this matter, but most geologists and geophysicists consider water to be the lubricant that makes plate tectonics possible. In a billion years or so, the Sun will have become 10% more luminous. This is conjectured to make the Earth to undergo an unstoppable moist greenhouse / runaway greenhouse, and the oceans will vanish.
The core is still emitting residual heat from the formation of the Earth. As the core cools, iron in the outer core freezes onto the inner core. This is freezing is an additional source of heat. The solidification of the Earth's core thus represents another permanent threat to plate tectonics. The liquid outer core is conjectured to have frozen solid less than three billion years from now.
A nearer term threat is the formation of the next supercontinent. Plate tectonics may operate in fits and starts. What makes subduction zones form is not known. What is known is that a major subduction zone vanished when India collided with Asia, and no new subduction zones formed elsewhere to take its place. If this conjecture is true, plate tectonics will temporarily stop in a few hundred million years when the next supercontinent forms, only to restart later when too much heat stress builds up inside the planet.
This is all highly conjectural. No scientist will live to see their conjectures falsified.
The whole plate tectonic system is good for a few billion years yet. David is correct that water, as a lubricant, is needed to keep the system moving, but a 10% warming of the sun isn't enough to completely destroy the oceans. That will occur, but not until the sun moves close to, or into its red giant phase several billion years from now. The other factor is uncertainty as to how long there will be sufficient radioactive heat to overcome viscous drag of the convective cells which underlie the crustal plates. There has been much speculation, but I am not aware of any convincing analysis of how long this will take.