Drupal 6.0 RC3 was released a few days ago. I was hoping that it fixed the issue I wrote about in this post but it doesn't. I spent some more time working on the problem and this time I tracked it down to the node_submit function in modules/node/node.module. When node_submit is called from modules/blogapi/blogapi.module then $node->teaser_include is not set. When $node->teaser_include is not set the node_submit function cuts the teaser from the body of the post and that causes the problems i described here. When a new post is created from Drupal's create content form $node->teaser_include is set and everything works the way it should.
I haven't managed to track down why $node->teaser_include isn't getting set when posting with modules/blogapi/blogapi.module. But there is a simple workaround, set $node->teaser_include before every call to node_submit in modules/blogapi/blogapi.module using this diff patch.