Just 3 or 4 potential problems here:
Seals become split, or brittle and need replacing
Thermostats fail. If you suspect this is the problem, by-pass the thermostat and the fridge should run permanently.
If it does, you will need to replace the thermostat.
Compressors lose gas. (Can be re-gassed)
There is a small electrical component near the compressor called a relay.
This actually "kicks" the compressor into life. If this fails, there is inevitably a nasty smell of burning. Replacing this item normally cures the problem. (The problem itself is often caused by the fridge being moved and not allowing the gas to settle before switching back on. A minimum period of 24 hours should be allowed.)
For further help with repairs, try www.howtomendit.com