Seems to be a common problem with the Moment. I exchanged a couple for the same reason.
In some cases, the phone would charge perfectly.
In some cases, the phone would report that it's charging, but it really wouldn't.
In other cases, the phone wouldn't acknowledge the charger, and wouldn't charge.
Some nights, I would be awakened by the notification sound of the phone connecting the charger, then disconnecting the charger.....continuously.
It was always a roll of the dice when I plugged my charger into the phone.
As someone else mentioned, it's an internal problem. If you're under warranty, get a new one. If you're eligible for an upgrade, now might be the time to ditch it.