Yes, Closers has a stamina system. Most dungeon runs will consume 10 stamina and it's usually 17 runs per day.
Closers will reset stamina at 4am KST or 2pm EST.
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The first 2 dungeons in GGV (1st area) consumes 5 stamina on easy mode,because they kind of belong to tutorials.
However,you can always do special dungeons on each area and EDMs (emergency defense missions) 3 times a day each even if your stamina is 0/170.