According to page-1268-69 of Halliday, Walker & Resnick's Fundamentals of Physics (10th edition),
To emit enough light to be useful as an LED, the material must have a suitably large number of electron-hole transitions....What we need is a semiconductor material with a very large number of electrons in the conduction band and a correspondingly large number of holes in the valence band. A device with this property can be fabricated by placing a strong forward bias on a heavily doped p-n junction, as in Fig. 41-16. In such an arrangement the current I through the device serves to inject electrons into the n-type material and to inject holes into the p-type material. If the doping is heavy enough and the current is great enough, the depletion zone can become very narrow, perhaps only a few micrometers wide. The result is a great number density of electrons in the n-type material facing a correspondingly great number density of holes in the p-type material, across the narrow depletion zone. With such great number of densities so near each other, many electron-hole combinations occur, causing light to be emitted from that zone.
Now, if electron-hole pairs are ceasing to exist due to recombination and resulting in a greater number of "gridlocked" electrons and light, who will continue to conduct electricity? Won't current flow stop after a while due to the absence of electron-hole pairs?