How to keep active class in main navigation when single post is viewed?

“Blog” in the first post is in class “current_page_item” while in the “blog” page in is in class “current_page_parent”. All is well.

You need to modify either style.css or header.php.

style.css would be better place for that.

Something like this (“not tested”, be sure):
div#navigation div.menu li.current_page_parent {
/* copy something from definitions for li.current_page_item */
}

HTH,

/dor