Do I need to make a roll each round I control the creature, or is it activated once and stays with me until dead. We started playing it, that I had to make a new roll every round to see if it didn't fall back to the earth. Is this correct? or should I assume that once I make the roll... he is mine.

The roll has to be made after every turn you take with the monster.

Per the card text: " after the monster completes its activation, the controlling hero must roll one power die. If he rolls anything but a power enhancement, the animated monster falls apart and is killed."

This clearly states that you roll every time you activate the monster (even if you don't activate the monster you still roll)