Digging in clay is always a pain. I started adding water to the hole first. It softens the clay so the digger cuts through easier. We did this on a job last month and saved a bunch of time. Just pour a bucket in and wait a few minutes. Then the posts set nice and solid. My crew swears by it now.
Oh totally, @the_zara is right about the timing! I found that sweet spot where the ground is still soft from the rain but not soupy. Makes digging so much easier.