These circular motions do more than transport heat to the surface of the star, however. They also transport the stellar material itself, which means that the material throughout the whole star gets all mixed around. So, due to convection, the helium which is created by fusion in the core becomes distributed throughout the star. Because of this, there is no build-up of helium in the core. Without a helium core, the star is not able to reach the helium fusion phase (also known as the Red Giant Phase). Instead, as the hydrogen is used up by fusion, the star loses the balance of hydrostatic equilibrium and simply contracts and heats up due to gravity. At this point, it is no longer a MS star (since it is no longer fusing hydrogen), but becomes a White Dwarf.
The main sequence lifetime of a red dwarf is about 100 billion years. Since this is older than the age of the universe (on the order of 10 billion years), these stars have yet to reach the white dwarf stage.
An illustration of a Red Dwarf.