I’m not sure what you mean by ‘not properly publishing’. Do you mean they don’t show in status ‘published’?
What happens if you go to the WP post list screen, select the posts, and choose bulk actions->edit, and then publish them? Do they go to status ‘published’ then? If not, then there is something unique about that post type. I don’t know anything about jigoshop so you might want to check their forums.
I can give you two general tips:
1. the correct status for import is ‘publish’, not ‘published’ – that sometimes trips me up
2. you could check the database table wp_posts and look at a post that was successfully published, to see if there’s something special about it, like a special post status