A relay sometimes makes a chattering or popping noise when it is about to fail. But often there is no warning.
It is difficult to predict the life of a relay. Relay failure is rare on some of the small 120 volt jewelry kilns, because they fire to low temperatures and have little amperage running through the relay. (One of the causes of relay failure is excessive heat in the switch box. The relay contains a small electromagnet with a spool of copper wire. Heat melts the thin insulation on that wire.)
On the other hand, firings with long holds or extended slow cooling segments shorten relay life. Cycling the relays on and off for long periods eventually wears them out.
A relay can fail in two ways: in the "on" position or the "off" position. If a relay fails in the "off" position, your ware will not fire to maturity. Ordinarily you can just fire it again.
If your kiln has two or more relays and one of them fails in the "on" position, your ware may slightly overfire, but the kiln will not overfire. If your kiln has only one relay and it fails in the "on" position, the kiln will probably overfire.
For long relay life, do not allow the firing room temperature to get higher than 110 degrees F (when measured 3 feet from the kiln). High ambient temperature is hard on the kiln's relays and other electrical components.
If you monitor the kiln near the expected shutoff time, you won't have to worry about relay failure. You will be there if the kiln doesn't shut off due to a stuck relay, and you can disconnect the power yourself. However, you don't have to constantly watch the kiln throughout the firing. Just check on it occasionally.