Blog is not designed to be used on mutiple pages and it is a problem to move it from one page to another.
Why?
Because it uses friendly urls that map to a real url with the page id included as an url parameter.
ie a blog post with url /my-cool-post.aspx is mapped to the real url /Blog/ViewPost.aspx?pageid=x&mid=y&ItemID=z
so when you move it to a different page the page id in the real url no longer matches the page that blog is on and security enforcement prevents viewing the page.
It can be fixed but it is tedious to fix it. You can go through each blog post url in Administration > Advanced Tools > Url Manager and change the pageid in the real url to mathc the new page.
Best to avoid this problem by not moving a blog after you make posts.
Hope that helps,
Joe