Business days are Monday through Friday and should not include Saturday or Sunday. Etsy doesn't take into account Federal Holidays, so those are included in the regular Monday-Friday day count.
Etsy considers orders placed on Saturday and Sunday to have the same 'ships by' date as orders placed the Friday before. If you have an order placed on Saturday with a 1-2 business day turn around time, the 'ships by' date should still be Tuesday though.
I've struggled with this shipping date challenge as I have a lot of weekend sales, which I don't technically find out about until Monday. My production time changes between 2-4 weeks depending on the season and it's frustrating to me that all the weekend and Friday orders would have the same Friday 'ships by' date.
If your orders placed on Saturday or Sunday were considered past-due or late on Monday, then you should contact Etsy since that should not happen. I believe the timing is set based on NYC time, so that may be part of the challenge if you are in a very different time zone.