The fuses are on the 12 volt side on the campers converter
. The converter converts the alternating current (AC) from shore power or generator to direct current (DC) from the campers low voltage systems.
My guess would be a power drop from your generator. If the problem doesn't occur on shore power then the gen set may be dropping off quickly when it's switched over. A drop in AC voltage to the converter will equal a drop in DC voltage of it's output. The lower output will then cause a quick momentary rise in amp draw to any connected device. That quick rise in amp draw can cause the fuse to blow. If the battery is waiting for a charge then it would be the hungriest and it make sense that it's the first to blow.
Visit your local rental center and rent a small inverter type generator for a day and perform a DIY test.