Confused about traverser stones

[cheyrn]

The number of traverser stone key items I have does reduce each time I use one, if I have been given stones by Joachim. After 3 I continue entering without having a traverser stone key item. And the very first time after being given 3 I have used 4.

After some number of times, over the course many days, I was told I did not possess a traverser stone. I immediately went to Joachim, got more stones and could enter right then after getting the stones.

So, my original question was what determines when you need to have a traverser stone key tiem, since it is not the number of stones I am given by Joachim.

The description of main storyline quests in Abysssea, on another website which rhymes with Eh fecks I encyclopedia:

You must have a Traverser Stone in your inventory to start the quest, or you will simply be allowed to enter with no cutscene.

Which implies that you are granted entrance even if you don't have a traverser stone. And twice I have caused the main storyline quest to start by leaving Abyssea, getting a traverser stone from Joachim and reentering Abyssea.