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I have a couple of questions for me to help figure this out.
1. Is this a two handle faucet?
2. How old a faucet is it?
3. Can you see any brand name?
It sounds like the hot water valve has come apart and is closing itself when it expands from the heat, etc. .
1. Turn the water off to the faucet.
2. Remove the faucet handle.
3. Remove the hot water valve cartridge.
4. The easiest thing is to just replace the cartridge with a new one as they cost approx. $10.00+/-. Or you can try fixing it by cleaning any crud that has become lodge in it or putting it back together properly if it is not totally broken.
5. Flush the water through the opening where the valve was by turning the water on to the faucet for a second or two to make sure nothing else is restricting the flow of water and then reinstall the new or repaired valve.
Let me know how you do and if you find something else out as you take it apart.