It could easily be the check valve (backflow preventer). They're often part of the city water inlet fitting and you may not be able to just replace the check valve. As suggested, remove the filter screen on the inlet on the exterior of your unit and push in the center of the valve to try and free it up. The screen only filters out course material and sediments could get past it and gum up the check valve. If this is the case, you might want to consider a sediment filter cartridge/housing.
FWIW, there are less expensive plastic city water inlet assemblies and ones made from solid brass.
JR Products city water inlets