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This is why I NEVER show my post on the home page. I hate themes that display the entire post on the home, category, and archive pages. They are terrible from an SEO perspective.
Instead, to avoid this very issue I use custom excerpts for my posts. The custom excerpts appear on the home page, category and archive pages... I don't even allow my theme to show the first XXX words of the post as an excerpt/teaser. The custom excerpt is written from scratch.
This phenomenon you're seeing with your post is another form of canonicalization issues (and duplicate content) where the "preferred" URL is really the post page itself but because the content also appeared on the home page and the home page has MUCH more power than an individual post page then Google thinks the version on the home page should be your "preferred" version of the post.
As chrishirst said, it will fix itself over time, but it's a very bad user experience. Users clicking on that might be taken to your home page and the post may already have rolled off the home page.
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