Constantly running air compressor for a Ruud electric heat pump What does this mean?

If the outdoor temp is around 35*or lower, it probably means nothing other than you are near the balance point when the unit should switch to auxiliary (electric) heat. At 35* or so & lower the heat pump alone can no longer extract heat from the ambient air effectively and you may also develop ice over problems on the outdoor unit. If these are not the temps you are experiencing when this occurs you should have it looked at.