The rate at which your hairs emerge from their follicles is constant, but the rate of increase of the total length of the hairs slows down and eventually stops because the hairs naturally wear down over time.

Imagine that your hair is like pasta being extruded into water, and that it slowly dissolves over time. The more time the pasta is in the water, the faster it dissolves—and it eventually reaches an equilibrium where the length stops increasing at all. But if you cut off the pasta at the extruder and time the new pasta coming out, it will be the full extrusion speed instead of the extrusion speed minus the dissolution rate.