Often refer water/ice lines were connected to the water supply with a saddle type valve that clamped onto the pipe and pierced a small hole into the pipe.
Over time, the valves and the small holes can become clogged due to mineral deposits. This is why it is much better to have a regular line, valve and perhaps a stainless braided supply hose tot he refer.
It would be a good idea to post it in the Appliance section in case it is an issue within the refer's components instead of a clogged supply line or valve.
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