My best guess is that you moved the blog to a different page than it was originally on or else created posts from within content manager without a page context. The same blog instance cannot be used on multiple pages and you cannot easily move it from one page to another. The reason is because the blog creates friendly urls for blog posts at the time when posts are created and those friendly urls map to real urls like
/Blog/ViewPost.aspx?pageid=x&mid=y&ItemID=z
and the pageid must be correct to enforce security, therefore you cannot change the page later and you cannot make a post without doing it from the blog while it is on a page. If you do that then you will get the permission problem you are having now because the friendly url mappings don't have the correct page id in the real url.
Hope that helps,
Joe