A wine cooler not holding its set temperature has different likely causes depending on the cooling technology.
Thermoelectric (Peltier) wine coolers — the small, quiet, inexpensive ones — have one core component: the thermoelectric module itself, plus the hot-side and cold-side cooling fans. A failed module means the cabinet can't cool at all and the unit drifts toward room temperature. Module replacement is possible but often costs more than the unit; at that point replacement usually wins.
Compressor-based wine coolers — Sub-Zero 400 and 700 Series, EuroCave, and the higher-end built-ins — have the same sealed-system architecture as a refrigerator. Most failures are on the electronic-control side: zone thermistors drift, thermistor wiring corrodes, evaporator fans fail, or control boards lose the ability to stage cooling correctly between zones on dual-zone units. These are routine repairs, typically $300 to $600 installed.
The good news on compressor-based wine units is that the compressor itself is almost never the failure. Wine storage runs under very light thermal load compared to a kitchen refrigerator — cabinet set points are 50–65°F and door openings are infrequent — so compressors in these units typically outlast the surrounding electronics by years.
Don't ignore a warm wine cabinet; storage temperatures above 70°F measurably accelerate wine aging and at 80°F-plus begin to cause cork expansion and seal failure.