Mark, your question is one of (soil) mechanics. You would have to calculate the lateral earth pressure on both the boards and the fence posts to answer it. You can find a nice introduction here.

Basically you need to know the failure plane angle (denoted by the greek small letter phi: φ) and the soil/wall friction angle (denoted by the greek small letter delta: δ). These values will depend e.g. on the type of soil, the amount of water in the soil and the amount of roots holding it together. If you look around you'll probably be able to find manuals or codes to help calculate such supports if you are so inclined.

Realize that all the forces from the soil acting on the boards have to be balanced by forces from the soil acting on the relatively small fence posts. My gut feeling would be that the posts are possibly too far apart.

This construction has at least the following failure modes;

• If the posts are too short (not far enough into the ground) and too far apart, the lateral pressure on the posts be too great for the soil to hold and will make them shift in the ground, making the whole structure topple. This is the most likely failure mode, IMO.
• If the distance between the posts is too long relative to the thickness of the boards, the boards might deflect too much and even break.
• If the distance between the posts is too long but the posts are deep and the boards are thick, the post might just shear off.

Corrosion of the metal posts and rot of the wooden boards will decrease the performance of the support structure over time.

One important point is to make drainage holes in the boards. Otherwise you would get additional water pressure, and water makes it easier for the soil to "flow".