Use a name tag on the armadillo
Keep the armadillo in a loaded area
Put the armadillo in a fenced or walled enclosure
Avoid moving too far away from the armadillo
Keep the chunk loaded with a chunk loader if available
Do not let the armadillo die from mobs, fire, lava, drowning, or falls
Make sure the world is not set to despawn entities through mods or server settings
On servers, ask the admin to check entity-clear or mob-despawn plugins
Keep the armadillo in a boat or minecart if needed
Save and exit only after the armadillo is secured and named