I have no answer, but I have some tips to better understand what is happening.
If you use Google Chrome, open the Network panel of the developer tools and see what happens when you log in.
Check which domain cookies are configured in, when you look at the response headers for a POST request that processes your login, you should see Set-Cookie headers, check if these domains are .domain domain. com or blog.domain.com and see if this request tries to redirect you to another place.
Another possibility is that your Wordpress installation may be configured differently than you want, for example, the website URL: www.domain.com/blog, not blog.domain.com
Is it possible for you to visit the login page at blog.domain.com/wp-admin/?
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