If the freezer was working correctly, running all the time should produce extremely cold temperatures in the freezer (-10°F and below!). Have you put a thermometer in the freezer to see how cold it actually is? Are frozen foods unusually hard?
If the freezer is NOT unusually cold after running continually, the appliance is not cooling properly and someone will need to investigate why. If the freezer IS unusually cold, there may be a problem with its thermostat (see the following link).
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