Currently, Im online right now, but I show a "red offline dot" when I clicked on my profile. I did check in my personal settings, and Im "show online to all" currently.
1. Why does this happen?
2. Can this interfere with my stats?
Well, if all else fails...just log out and then log back in. Apparently that fixed it. I was online for quite a bit of time, and I wonder if that had anything to do with it. I was online but it showed I wasnt. So, logged out and tried again, and now it shows online. Weird...
I've noticed that happen to me most every night around this time and I do as you suggested, log out and then log back in. Once I do that, the green dot returns and my stats continue to advance, but if the dot is red, stats don't seem to get updated.
I believe there's a timed out function. If you walk away while logged in for certain amount of time the website logs you out like your bank. Dont know the exact time that is set. But it has happened to me a few times when I left the house and forgot to log out.