Thermocouples are devices using metal alloys that produce an electrical current when subjected to heat -- measuring this current allows it to be used as a temperature gauge. Thermocouples are often used as regulators in home furnaces, for example. As solid state devices, thermocouples are relatively resilient; premature failure generally comes from a combination of problems.
Because a change in temperature results in a slight variation in size over long periods of time, these constant cycles of expansion and contraction can cause "metal fatigue." In other words, the thermocouple becomes less and less resilient until it finally breaks. This process can be detected by monitoring the thermocouple for unusual readings, especially if it's in an environment where it is subject to repeated heat stress or extreme temperatures.
If the thermocouple is a sealed environment, as is used in ultra-high temperature monitoring devices, any exposure to the atmosphere can exacerbate natural decay processes, leading to premature thermocouple failure. Oxygen in the environment reacts with the pure metal of the thermocouple, making the wires thinner and potentially more brittle: as the oxidation grows worse, it exposes more and more of the thermocouple to attack. Even a small amount of oxygen can cause problems, so a sealed thermocouple should have its environment checked regularly to make sure that it has not been compromised.
Even if the thermocouple is not highly sensitive to atmospheric intrusion (as helium-filled thermocouples are), it can be prematurely damaged by contaminants. Sulfur is particularly problematic for thermocouples made with pure nickel; at high temperatures, it reacts with the nickel to form nickel sulfide. Many problems leading to premature thermocouple failure -- including metal fatigue -- can be exacerbated by impurities in the thermocouple, caused either during the manufacturing process or by user error when installing or handling the device.
One of the leading causes of premature thermocouple failure is simply poor installation, which can make any other problem much worse. Thermocouples need to be precisely placed and protected. Otherwise, they may be subjected to stress beyond their design tolerances, or they may be brought into contact with chemicals that reduce the effectiveness or strength of their materials. This is particularly true for home thermocouples, which are frequently placed in furnace rooms that lack the cleanliness and uniformity of a scientific laboratory.