After being killed once, the pillagers don't respawn in their outposts
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I have made a test, put my world in creative and in pillager outpost write in the prompt "/kill @e", so every mob and pillager was killed. So, after some time, I see that pillagers are not spawning, so I tried to see during night and have seen that pillagers are only spawning during night
Edit: I have take a more deep look into this, and seen that only respawn one pillager, and nevermore pillagers are spawning until you change game difficult to peaceful and then back to hard