Laurel,
If you are on shore power or if the generator is running, your inverter should recharge your house battery bank. If not, either you have the charger function disabled (turned off), or the battery charging section of your inverter is defective.
Sometimes, you can disconnect all power (12 volt and 120 volt) to the inverter for about 30 minutes and it will restart and function properly, especially if you have a Xantrex inverter. That is rare for a battery charger malfunction, but it is a easy fix if it works.
Gerald