One of the most common reasons for element failure is loose connectors.
Paragon element connectors should be tightened to 30 inch pounds. This is about 1 1/4 turns past the point of firm resistance.
A loose element connector will get too hot, which can turn the connector a greenish color. (Sometimes white.) If you observe this on your kiln, you can try tightening the connector. However, since the element has already been fired, tightening the connector may break the element. This is why it must be tightened properly at the time of installation.
If, when tightening the element connector, you feel the threads strip out, remove the connector. Install another. A connector with stripped threads will be too loose. Suppose the head of the screw or bolt on the element connector twists off? That's okay, as long as the threads are still holding.
Use locking pliers (i.e. Vice-Grips) to hold the barrel of the connector while you tighten the screw. Then tighten the hex-head screw with a 1/4" nut driver. You can grip the screw better with a nut driver than with pliers.
Another important point: after installing the element, cut off the element end even with the connector. I have seen cases where the pigtail shorted out inside the switch box because the end wasn't cut off.
You can probably find a use for the pigtail ends. Some people untwist them and use them for element staples.