[courtneyehart]

My GE compressor is not staying on. It will go on and make the fridge cold enough but will not stay on. It gets cold long enough for ice to melt but when the compressor turns off, it stays off for so long that the ice melts and the temperature goes up. In turn the fridge doesn't stay cold enough to keep food. I have cleaned out as much dust as possible but that didn't seem to help.

[denman]

Here are your parts, you seem to be short a few digits.
Replacement parts for TFX27PP models | AppliancePartsPros.com

Check that the condenser/compressor fan (Item 650 in Section 6) and the evaporator fan (Item 610 in Section 3) are on when the compressor is on.

Since the compressor does cycle it sounds like the thermostat (Item 424 in Section 4) is sticking open. The next time it happens give the thermostat a tap or turn if up/down a bit. If the compressor fires up I would replace the thermostat.