Hello & Welcome to Just Answer,
I'm Greg and will do my best to assist you today.
Sorry to hear of any issue you are having with your phones.
To help you with this issue, may I ask:
1) Can you CONFIRM that your AT&T system has a built-in Answering system, and that system is normally ON - to answer your missed calls.
2) What phone service provider (phone company) you have for this phone line?
3) You also mentioned "voicemail", so does your service provider offer a voicemail system feature?