One thing I’ve noticed is that when I log in, it takes me to the home page, which almost *never* reflects that I’m logged in, but as I navigate to the articles they acknowledge that I previously logged in and allow me to comment 90%+ of the time. On the times that they don’t, here is my process:
1) First I refresh the page. Frequently, it re-loads and acknowledges your login.
2) If that doesn’t work, I attempt to log in via the “You must be logged in to comment” link. Since this doesn’t re-route you through the home page it may have a higher success rate.
3) If neither works, I give up and come back to the article later and for some reason it works again (but one that was working earlier may have stopped).

Obviously this isn’t a user-friendly solution and I am not presenting it as a permanent or acceptable way for commenting on the site to work, but simply suggesting options as you navigate/troubleshoot. The more data points we can get on people trialing the site and finding out when/where it’s not working, the closer we get to a meaningful investigation of the what/why, which then our dev can fix.