[Domain Mapping} Cross Domain Auto-login not working

The Cross Domain Auto-login feature in Domain Mapping doesn't seem to be working on my multisite network. As far as I'm concerned, once I'm logged into the primary site, I should be able to access other sites without entering login credentials. But that's not happening. I understand that the cookies might not be able to set on all sites if the number of sites is too much, but I just have 5 sites which are mapped. Here are the steps that we've tried:
1. Commenting out DOMAIN_CURRENT_SITE.
2. Using default .htaccess.
3. Running a full plugin/theme conflict test.
4. Enabling debug.

I was able to see the following log entry in the debug.log file multiple times generating consistently: https://pastebin.com/Eswy2bPt

Not sure how much relevant it is. Please advice.