My guess is:
Below the ground and in the air,
You can find a creature hiding there.
The moon can be overhead or on the otherside of the earth
Above you now, not found below,
Indeed before, before any go.
If it's overhead it isn't on the otherside of the earth
After now it will hide away,
Never in a day does it stay.
It will be on the otherside of the earth within 24 hours
Missing only once in all.
Missing due to eclipses which are rare.
Changed appearance! Now don't fall.
Looks brighter and closer on full moons, but if it got too close and fell to the earth we would all die.