If I get Core Aura green, will it degrade back to blue on its own?

I'm trying to decide if I should even bother with Core Aura anymore since I don't spend money on the game.

I know it's possible to get it green through free dust since I did it before, only to get it back to blue trying to upgrade it further. But I don't know if it would have degraded on its own anyway.

Does it?

Yes it can degrade naturally regardless of rank (color).