a. Introduction
The first time my equipment broke from enchanting a level 2 puzzle made me wonder.
Is it that the enchanting rate is not 95%? Or am i just unlucky?
I've decided to experiement with all the equipments i picked up from mobs and enchanted it with level 1 puzzles to see how "unlucky" i was at enchanting. While i was doing this, I've come up with an idea.
I call this theory, the Enchant Cycle.

b. Experiment
Note: Numbers below the trials represent the time that an item broke while enchanting.

Trial #1
14th
Trial #2
3rd
Trial #3
17th
Trial #4
12th
Trial #5
21th
Trial #6
3rd
Trial #7
12th

According to my personal experiment, two out of seven trials broke while enchanting on the third try.
The point of this experiment is to show that the chance of your item breaking at anypoint is 100% random.
P.S. Those three happened to be my sphinx head gear with extra str stats and Latale Ely high durability by the way.

c. 1ndex's Question for You

What are the chances that the item you enchanted will break twice in a row?

d. The Enchant Cycle

EC (Enchant Cycle) is the process of upgrading valuable items such as King Goblin Accessories successfully.
EC ensures more success rate to the process of enchanting any item.

The process of ECing is the following.

1. Break an experiemnt equipment purposely by enchanting
2. As soon as an equipment break, enchant the item you want to EC.
3. Break another experiment item purposely by enchanting
3. As soon as an equipment break, enchant the item you want to EC.
4. Repeat EC

If you are impatient to EC one at a time, you may try risking yourself by ECing every 2 items.

1. Break a experiemnt equipment purposely by enchanting
2. As soon as an equipment break, enchant the item you want to EC.
3. Enchant the item you want to EC again.
4. Break a experiemnt equipment purposely by enchanting
5. Repeat EC

I do not recommend you go for the third time due to the fact that i've broken my equipments before Latale Ely trying to enchant for the third.

e. Conclusion
Enchanting itself is luck.
EC is made to push your luck to its maximum.
There's still a chance that your item might break even when ECed.
The Key to a successful ECing is patience.