Just to make sure we're talking about the same thing, this is the Evenheat Kingpin 88, listed as a metal clay kiln?
From what I can see in the manual, it says the elements are located in the left and right walls. Perhaps you can put an oven thermometer or some other method to see if one of the walls is getting hot and the other not. That would help troubleshoot. Assuming that each element has its own relay, it would not tell you whether the problem is an element or a relay, though. (OK, since there is only one relay, this might help determining if it is an element. The elements are in parallel, so another possibility is the wiring between the elements. See diagram linked below. There are jumpers between E1 and E3, and E2 and E4.)
Hopefully it is a relay, since the elements are embedded in the walls.
Never mind, there is only one relay
http://www.evenheat-kiln.com/pdf/wir...in-88-120V.pdf
If you can get it to temperature, then, in my opinion, it is sounding less like relays and elements than the thermocouple/thermocouple connection. (I guess that's being hopeful, because by Evenheat's info, it is sounding like elements, but hopefully Eric's experience with relays is correct because embedded elements are expensive.)
More Evenheat information, which you might already have:
Kiln Fires Too Slowly
Elements are wearing out. Elements age when fired and increase in resistance. Firings gradually take longer, and longer until the kiln will not reach temperature. Replace all elements. High firings wear the elements out faster than lower firings.
Make sure all elements are firing. You can check this by carefully lifting the lid while the kiln is on to make sure all elements are glowing. In some kilns, especially automatics, the top and bottom coils appear to become hot quickly while the center elements appear to be slow in becoming hot and are less bright. Do not touch the elements when doing this!!
Voltage too low. As voltage falls so does power. Check voltage while under load for a more valid reading.
Improper operating voltage. Check rated voltage (printed on nameplate) against the measured voltage. A kiln designed for 240V will be slower when connected to 208V.
Voltage may vary in certain areas due to heavy electrical use. This is especially true in the summer with a heavy demand for air conditioning and refrigeration.
Long runs of wire from the main service can cause lower voltage, which lowers power.
High amperage draw of the kiln could cause a voltage drop at the kiln. While rare, this would indicate that the electrical service supply transformer is not capable of supplying the desired power.
Service wired incorrectly. The kiln may have inadvertently been connected to 120V instead of 208 or 240V. (It's happened)
Loose connections between fuse box and kiln.
Aluminum wire has been known to cause some problems. We do not recommend aluminum wiring.
Here's some pricing:
http://www.evenheat-kiln.com/pdf/ret...-clay-kiln.pdf
Hopefully not this, since these are the elements
Kingpin 88 Replacement Muffle
#00314.100
$279
Thermocouple For Kingpin 88
#11639.000
$11
For TAP, Set-Pro & RM Models
#11801.200
$35