Hello & Welcome to Just Answer,
Sorry I didn't see your question earlier and to hear of the issue you are having with your phones.
May I ask:1) The FULL Model Number of the phone system you are working with?2) How many TOTAL handsets do you have with this system?3) What phone service provider (phone company) you have for this phone line?4) If you have ANY other devices (phones, fax, alarm system, etc.) attached to this same phone line (not part of the cordless system)?
5) Can you VERIFY that the Answering System feature of the phone system is turned ON? MOST Panasonic phones with answering systems have an "ANSWER ON/OFF" button on the MAIN BASE UNIT of the system, so I would start by checking there.