RV fridges are, at their core, rather simple devices. The cooling system either operates or it doesn't. (The control system can be a little more complicated.) If it's cooling properly now, then nothing major in the cooling unit is broken. (There's also not a lot to break down; it's not as though ammonia or water or hydrogen gas wear out over time. So long as the unit is level and the fluids are flowing properly and the piping isn't perforated, it will keep working.)
By the way, you'll save a good bit of electricity if you use a standard household compressor fridge for your extra fridge rather than the RV fridge. The RV fridge uses somewhere in the general vicinity of 5+ kWh per day, which for me would mean somewhere around $350 in electricity in a year. A normal (energy star rated) fridge uses somewhere around a fifth as much electricity. Something to think about....