A fair number of them I believe, but if the top inch or two of your soil has a chance to dry out between waterings/wettings I'd think they weren't the culprits. Is it possible to keep the surface soil dry for awhile and bottom water only? If it is, I'd move it to part-shade and try that (depending on your local conditions, of course). If you're getting regular rains, then maybe not.
If you aren't watering daily - are there any signs of critters digging in it? I had some seedlings that looked rather peaked for a while because a rodent planted sunflower seeds right next to them. If they cover up the hole it's easy to miss the loosened soil. We've had no rain this year, but I still don't water more often than every other day (and usually longer than that), so my disturbed seedling's roots had time to dry out a bit. Damaged, but salvageable.
