How to stop paneling cracks around air vent

You would have to remove the cracked boards (what you show appears to be what is normally called "bead-board," a subset of tongue-and-groove boards, rather than what is typically meant by solid wood paneling, where "panels" are in "frames"), glue them together properly, and replace them - or just replace them with intact boards.

When doing that you need to install them in such a manner that the tongue-and-groove edges are free to move as the boards expand/contract. This wall appears to have been painted over in a manner that has "locked" the tongues and grooves with many layers of paint, and when the boards shrunk the weaker spot was out in the middle of the board, so it cracked, as opposed to the movement happening at the joint.