Your going to want to bring a multi meter with you to measure your battery voltage. When your trailer is plugged into power it produces 12v DC for your lights. When you unplug the trailer it will be using the battery. So if everything stops working when you unplug it means your battery is dead, or a wire is loose, or the connection is corroded. Measuring the battery voltage when you go back will answer a lot of questions.
The reason everything seems to work normal for 1-4 weeks, must be because you are plugged into a power outlet while camping?