Permalink redirect issue in WordPress

My WP website is currently set to use the following permalink structure:

http://websitename.com/%postname%/

If I change that it to:

http://websitename.com/%year%/%monthnum%/%day%/%postname%/

everything works correctly. Specifically, older blog posts posted elsewhere (e.g. my FB page) redirect to the new URL automatically.

However, if I use a custom permalink structure and set it to the following:

http://websitename.com/blog/%postname%/

the redirect does not work on older posts. That is, I can still access all of the posts from the site, but if I linked to one of my blog posts on my Facebook page, for example, the old URL produces a 404 and does not redirect. I am thinking it has something to do with “blog” not being one of the variables that WordPress recognizes.

Any thoughts on why this is happening, and how to fix it?

Thanks in advance!