Pillagers and illager captains don't respawn around the outpost. Sometimes they do respawn sometimes they don't.
This issue was fully fixed in 22.214.171.124 Beta on Android, but partially fixed for Windows 10. In Windows 10, killing the captain that initially spawned in an outpost will not respawn anymore, normal pillagers respawn properly but not the illager captains. If you are experiencing an issue where illager captains don't attack, see