I loose power only when we are home and only on one circuit. The breaker does not trip. I have replaced all the outlets I know of on the citcuit. After a while the power comes back on its own on that circuit. This happnes randomly.

It could be the circuit breaker or the neutral connection in the panel.

If not that it might be a bad splice someplace or another device that is on that circuit, that you don't know about.

You have a loose connection. If you have replaced every device on the circuit then it could be in the panel. If there are any lights on this circuit then check them and their switches. The problem could be in there as well as a receptacle.