If you don't accept third-party cookies on your browser, that might be the problem. At least that's what Google Blogger product forum tells me. Because of course, Google intends to know all about you and where you have been. I've tried all sorts of options with no luck.
My helpful Canadian reader found something called Disqus, which you can add to use for comments instead of using Blogger comments. Unfortunately, it was too complicated for me. It would have required my doing some fooling around with HTML, and that always scares me.
I know Wordpress is a popular blogging platform and I tried it once, but I just didn't understand how to change a couple of things out and finally gave up.
Maybe you have figured out by now that I'm a simple person who likes everything to be easy. It is frustrating when people cannot comment here, and also frustrating that Google insists on tracking people so closely. Believe me, if I ever get Wordpress figured out, I'm moving.