In addition to what @ngurney suggested, a few other possible causes that you can look into:
# ***Ice Maker Control Module or Control Board***: The control module or board governs the ice maker's functions. If it's malfunctioning, it could be sending incorrect signals to the water inlet valve, causing it not to open after the first cycle.
# ***Clogged or Frozen Water Line***: Even with good water pressure, if the water line that feeds the ice maker is partially clogged or frozen, it could restrict water flow. You could try defrosting your fridge or checking the line for blockages.
# ***Faulty Water Inlet Valve***: Even though you're hesitant to replace this due to the cost, it's possible that the water inlet valve could be faulty. This is especially likely if the valve is a dual one, as you mentioned. It's possible for one side of the valve (the side controlling water to the ice maker) to fail while the other side (the side controlling water to the water dispenser) still works fine.
# ***Thermostat Issue***: If the thermostat within the ice maker is malfunctioning, it may not be triggering the refill cycle correctly after the first batch of ice is made.
# ***Solenoid Valve***: The solenoid is essentially an electromagnet that, when energized, opens the valve to allow water to flow into the ice maker. If it's not functioning properly, it could prevent the water from flowing after the first cycle. As you've mentioned, you can hear the solenoid coil energize, but no water flows after the first cycle. This might indicate that the solenoid isn't opening the valve as it should, or it may not be maintaining the open position for the required duration to let enough water in for ice formation.
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This may help you out as well: https://s3.amazonaws.com/sm-backend-production-attachments/service-manual-w10901168-bella.pdf?fbclid=IwAR3s3N_zPFAbH5GLKrOtebAfVSpljC_03W5YGNRoCS1wO6YET70YgzBOFoY
In addition to what @ngurney suggested, a few other possible causes that you can look into:
# ***Ice Maker Control Module or Control Board***: The control module or board governs the ice maker's functions. If it's malfunctioning, it could be sending incorrect signals to the water inlet valve, causing it not to open after the first cycle.
# ***Clogged or Frozen Water Line***: Even with good water pressure, if the water line that feeds the ice maker is partially clogged or frozen, it could restrict water flow. You could try defrosting your fridge or checking the line for blockages.
# ***Faulty Water Inlet Valve***: Even though you're hesitant to replace this due to the cost, it's possible that the water inlet valve could be faulty. This is especially likely if the valve is a dual one, as you mentioned. It's possible for one side of the valve (the side controlling water to the ice maker) to fail while the other side (the side controlling water to the water dispenser) still works fine.
# ***Thermostat Issue***: If the thermostat within the ice maker is malfunctioning, it may not be triggering the refill cycle correctly after the first batch of ice is made.
# ***Solenoid Valve***: The solenoid is essentially an electromagnet that, when energized, opens the valve to allow water to flow into the ice maker. If it's not functioning properly, it could prevent the water from flowing after the first cycle. As you've mentioned, you can hear the solenoid coil energize, but no water flows after the first cycle. This might indicate that the solenoid isn't opening the valve as it should, or it may not be maintaining the open position for the required duration to let enough water in for ice formation.