I think I may have a solution that will work for your site with the Oxygen theme. First a bit about how the Showcase template works:
- It displays recent posts in reverse chronological order.
- It will always display the three most recent posts under the "Recent Articles" heading. This cannot be changed.
- The remaining recent posts will be displayed under the "More Articles" heading. You can change the number of posts displayed here, but it will also affect other parts of your site like category and tag archives.
How many posts does an issue normally have?
If the answer is close to 10+ then this solution might work really well.
When you release a new issue containing 10 posts, the latest three will display under "Recent Articles" leaving us with 7. You can trick the "More Articles" section into displaying only 7 posts by adjusting the value of the "Blog pages show at most" option found in Settings → Reading. This will make sure that the older posts from the last issue do not display on your homepage.
In the event that each issue only contains about 4 posts, this solution may not be the best because your archives and search results would only display 1 or 2 posts per page.
Please let me know if this makes sense and if you think it will work.