I've been having an absolute bear of a time trying to figure out why I would get a login loop when trying to log into a wordpress multisite subdomain/subsite.
I finally figured out that when I went to map a domain to the new site i was putting in the wrong site id. In the latest update they removed the column that shows what the site ID is. I assumed that you just counted how many sites you have and however far down on the list it was denoted the site ID. If you hover your mouse over the site name in the sites list it will display the site ID then.
This is what worked for me and if i explained it wrong and anyone needs clarification please feel free to ask.