The hot water quit running to two of my hot water faucets. It works fine in the rest. What would cause this to happen? It used to work with no problems in all the faucets.

Sounds like you have mineral build up that's broke loose from pipe walls or from a water heater that hasn't been serviced and is now clogging the hot water inlets of the faucet cartridges. Turn the water off to the faucets and open them up. Check and clean the inlet ports . And before you button up turn the water back on for a minute to flush out the supplies and open valve body. Do this on both faucets. And if you don't service your heater let me show you how. For long life and fewer troubles you should keep your heater clear of mineral build-up by FLUSHING NOT DRAINING on a regular schedule. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white or yellow grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures that are affected . Now pull each aerator and clean the screens. Be sure you put them back togather the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. Hope this helps, Tom