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The Final Fantasy XIV Lodestone has been updated with a new "Ask the Devs" feature. While very short, the new article gives some useful information about the gathering process. Included are questions about wait times, flashing 'gather' notifications and more.
Even after I finish gathering and receive the "There is nothing left to gather at this location" message, the gathering point continues to flash, as if there were something still there. No matter how long I wait, though, I cannot gather there again. Why is that?
A. To prevent the exploitation of Eorzea's limited resources, Disciples of the Land are encouraged to visit several locations, rather than continuously deplete a single area. After gathering from one point, try visiting others. In time, you will find the first point will become available again.
Read more here.