Same issue, started for us on June 22nd. Publishing was fine on June 18th, then it broke. We are still struggling with the problem as the solution provided by ESRI Support (4th level) is a work around. Case #03090371, and bug #000150632. My suggestion is to start a case for your situation, maybe someone will begin listening, so far the case and bug submitted for us by ESRI support, was summarily dismissed by ArcGIS Online. There does seem to be a work around but it is tedious and time consuming. I'll say it again, upgrades, enhancements, and improvements should NOT BREAK stuff that already works for users.
