This is tricky. Microsoft changes things between versions and we're not always informed of what exactly changed. So in the case of server upgrades (SharePoint 2007 to 2010) and client upgrades (InfoPath 2010 to 2013) the form designer will most likely need to go thru a brief test phase to ensure the forms still work after upgrade.
There was another question on this web service posted today, but unfortunately it's hard to know what exactly broke in the Microsoft upgrade.
One troubleshooting tip I can provide is to design a test form in the new environment (IP 2013, ShP 2013) and recreate the troublesome data connections. Look for differences and hopefully identifying these will warn you of potential issues in the main form(s). Even a small change in the formatting of the Account can cause issues. Sometimes something as simple as walking through the data connection wizard fixes the connection, but sometimes a new data connection is needed. Sorry, it's hard to tell.
Let us know what you discover in your troubleshooting. Thanks.