When a mini refrigerator stops working, check to make sure it's plugged in, and attach other appliances to the outlet to make sure it's functioning properly. Feeling around the unit to tell if it's warm or cool can indicate the nature of the problem.
If the unit is plugged and isn't producing hot or cold areas, one of the mechanical components probably doesn't work. In some cases, the compressor itself may have failed, and replacements might be difficult to find. The compressor is typically the most expensive part of the refrigerator, so replacement may be the better option. Another possibility is a problem with the refrigerant, but be careful when tampering with this substance, since it's illegal to let it leak into the environment.
If parts of the refrigerator are producing hot or cold areas, the problem likely lies with one of the fans on the unit. In some cases, removing an obstruction from the fan can fix any issues. If not, replacement fans can be easy to install if they don't require too much disassembly.
Mini refrigerators generally work like standard refrigerators, but refrigerators used in RVs that are powered by propane tend to use chemical cooling. Troubleshooting a propane refrigerator requires expert help, since the chemicals used in it can be dangerous.