It’s a recommendation because it takes so long to cache posts. If you preload too often you might as well not preload at all unfortunately.
The best thing to do would be rewriting that plugin so it outputs a .js file that can be loaded by your blog. It’ll be update as soon as time changes.
Or just don’t worry about it because the “On This Day” output will be right for those visitors who aren’t near your timezone. 🙂