I've been advising people with various problems with accessing and maintaining Blogger blogs, that involve cache and cookies, for a while. Recently, I explored the ongoing problem with Blogger Stats and the "Don't track my pageviews" setting. Besides the known (and widely argued) problem with blocked third party cookies, I discovered a similar problem, with cookies being cleared when the browser is closed.
Besides Stats, it appears that the Blogger login process, and authenticated commenting, are also sensitive to blocked cookies / scripts, and to inappropriately cleared content. If clearing "cache and cookies", which is now generally known as "private data", is part of your browser optimisation or security strategy, you may wish to examine your policies carefully.
If you want to avoid problems with Commenting, Login, and Stats, you need to remove private data, selectively. And after removing cache and / or cookies, always restart the browser.