Since the heater core has been replaced and you are loosing antifreeze the next probable item for failure would be the hoses, or clamps going to the heater core. It is possible the heater core replacement was a defective unit, and I would start with the mechanic who did the heater core and ask for a check of the system describing it as you have posted here. Most mechanics I know want a good word of mouth recommendation, and letting him/her know you had this work done and still have a problem and if they can fix it will encourage you to send more people their way!