Well, what I’m trying to tell you is I believe the excerpts are a product of the creation and/or editing of the posts. I don’t think posts are exported with much other than the text, the images, links, and what would be necessary to recreate the post itself in the importing site.
Excerpts are more of a meta-type entry and dependant on their next environment which may be some system that doesn’t use excerpts or a theme that doesn’t need them.
If you want the exact copy of your posts on to the staging site then you need to copy over the whole database or else the parts of the database containing that info. A migration plugin might suit you better.
I mostly hate staging sites due to the many issues I see people run into with them. Yet half of the crazy stuff I do here involves what could be considered staging site(s).
Why don’t you drop into a post with your preferred editor and change just a tiny bit of something in one post and see if I’m right or not… I’ve been wrong before.
Another option might be to take your imported posts to draft or pending status then hit the publish button and see if that rebuilds your excerpts. And like I said, a migration plugin might suit you better here.
If you intend to continue using your staging site for content creating you might want to look at a syndication or RSS import plugin. Those usually ‘publish’ as opposed to a simpler import. The ‘publish’ is key I believe.
If it turns out I’m wrong then you might want to suggest the core team look at the issue.