Only two feet deep? That just seems crazy shallow to me, especially for any kind of fence or structure that needs to last. I always heard three feet was the absolute minimum to get below the frost line around here.
Read an article last week about post depths for different soil types. It said in clay soils, two feet might be okay if you pack it right. But they stressed that frost lines vary by region, so local codes should guide you. For example, in my area, the frost line is 30 inches, so I always go deeper.
Wait, only two feet deep? That's wild for anything that needs to stay up in bad weather. I've seen shallow posts heave right out of the ground after one rough winter. You must have some perfect dirt.