when using eyes of ender to track down a stronghold, the eye of ender will always lead to the same stronghold even if it's enderdragon has been beaten. No matter what when using eyes of ender it is only possible to locate 1 of 3 strong holds available to the players world.
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The Eye of Ender moves in the direction of the closest stronghold. Strongholds are centered around the original spawn point, so try going to the spawn point, moving a couple chunks away from the stronghold you know the location of, and throwing an EoE. It should then move towards a different stronghold.
Regardless, as Stefan said, there is only one "End" dimension per world, and only one Enderdragon. All End Portals in the overworld take you to the same spot in the End.
There is only one enderdragon per world, not one for each stronghold. If you beat the enderdragon and enter the End through another portal, you won't find another dragon.