Never touched the base (two pitches)

[CZ]

OK, sure the appeal must be made before the next pitch. But, the runner didn't officially miss second by 7.10 UNTIL the next pitch. He didn't touch bases out of order until he advanced to third which happened on the next pitch.

Remember that he kept his lead the whole time (bad idea but these are kids) between pitches so he has still never touched the bag. By rule he has not acquired it. On the next pitch he has only ever officially acquired first and his advancing to third is NOW touching bases out of order by 7.10. So the appeal is valid now.