Batting Order with Continuous Play

I have a very confusing question with several interpretations maybe y’all can help.  We play continuous order batting.  We had a team decide to skip a player that was on the order batting 10th which happened to be the last batter in the order. Our manager realized this and didn’t protest as the understanding was that once a player bats out of order then the new order is established.  If the new order has been established the next time through the order the team decided to have the previously skipped player bat in the 10th spot.

 

1.  Was the batter a eligible batter under the circumstances?  If so was the batter in order considering that the new order was established with no appeal in the prior at bat?

this player that was skipped was neither injured, sick, or absent.  Any thoughts and rule references would be helpful.  Thanks!