First off, you may or may not have an inverter but the thing that charges the batteries is the converter-charger.
The first things I'd check are the output of the converter-charger and the condition of the batteries (a simple voltage test comparing the voltage when plugged in and the voltage with the trailer unplugged to start, and a check of the "float" voltage of each of the batteries with the cables disconnected.) One or both of your batteries could be bad and soaking up part of the converter's capacity, or the converter may be giving up. Use a decent multimeter for this.
If the batteries are indeed 9 years old, it's likely that it's time to replace them in any case. I'm assuming that all the lights are still the original incandescents, and in a long trailer with lots of lights there can be a pretty big lighting load, but the batteries and converter SHOULD be sized to supply the trailer's systems.
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill