You may have to rebuild the faucet. It sounds like an anti-scald faucet. If you had the model number I could give you a better guess. But, this is a standard problem with the first generation of the pressure balanced faucets. The parts on the inside get worn and do not work like new. Its not too difficult to rebuild if you buy the proper parts from your local plumbing supplier. It even comes with instructions for installation. You can take a picture of the faucet and show it to the city desk and they will be able to identify the faucet and suggest the proper parts.