A freezer can fail to keep food frozen for a variety of reasons. Some repairs and solutions can be addressed by the layman, but others should only be undertaken by trained technicians. Before randomly attempting to diagnose the problem, it helps to understand, in a basic sense, how a freezer works and have a logical strategy in mind to trace the problem to its source.
There are two places you should begin your troubleshooting process, because these issues are easy to spot and simple to fix. The first is the thermostat, which may simply need to be turned to a colder setting. Lower the thermostat and wait a few hours to see if it solves the problem. If not, the next order of business is to check the defrost timer. Use a screwdriver to manually advance this timer out of it's defrost cycle to see if that's what is causing the defrosting issue. Wait an hour or so to see if the compartment grows noticeably colder.
Checking appliance wiring can be a tedious experience and no one will blame you if you decide to hire a professional electrician for the job. A single broken wire anywhere in the system could cause the entire freezer to fail. Cold air is generated only when an unbroken channel of electricity is available to power the separate parts: evaporator, condenser and compressor.
Mechanical parts of the freezer that can go bad include the compressor, evaporator and condenser. If you decide something is wrong with one of these, unless you're a qualified technician, you shouldn't attempt repairs yourself. Plus, the cost might be so prohibitive that it would make better financial sense to buy a new appliance. The compressor is the engine that drives the process and, if it is working properly, you should be able to hear it running, humming or making some sort of continuous noise. Also, check to see if the evaporator coils are iced over. A thick buildup could prevent proper temperature of the freezer compartment.
While frost buildup can create havoc with the evaporator coils in particular, you should also be aware that buildup throughout the compartment can block vents through which cold air is intended to flow. Resist the urge to defrost with an ice pick. Instead, relocate the food you have inside while you shut off the freezer, open the door and let the ice thaw naturally.