I had a similar problem and it was the converter overheating. I wound up replacing the converter. Most, if not all, converters have a built in cooling fan that kicks on to remove heat from the converter as it operates. Depending on the load on the converter, the fan will kick on and off. In mine, when the converter was supplying power to the battery and other DC components (lights, etc) the voltage output would be about 13 to 14 volts. When the converter shut off due to overtemp, the lights reverted to strictly battery voltage, about 12.6 V. This converter shutdown caused a noticeable decrease in lamp intensity.
In my bad converter, the cooling fan operated but the converter module was obviously shutting down even with the fan blowing. The shutdown would last about 5 minutes, then come back on, lights would get brighter and process would repeat in a few minutes.
Replacement converter fixed the problem.
