The time that is left until an armadillo drops its scute is not saved to the armadillo's data. This has two effects:
The scute drop timer cannot be modified via commands
Reloading the world resets the scute drop timer
A chicken's egg timer is saved to its data, so I would expect the armadillo's scute drop timer to be as well.
Confirmed. Relates to MC-265933 (skeletons' "in powdered snow timer" not saved, causing stray conversion to reset on reloading the world).