The way FeedDemon works is that it only does a "full" sync - which includes changes to read/unread items, starred items, tags and shared items - at startup and then once an hour. In between it does "incremental" sync, which primarily checks for read/unread changes since the last sync.
This makes FeedDemon's synching very efficient, at the cost of not immediately showing changes made outside of that copy of FeedDemon. For example, if you star an item in Google Reader (or another application that syncs with Google Reader) while FeedDemon is running, that star may not show up in FeedDemon right away. But it will show up during the next full sync.
If you want changes made outside of FeedDemon to show up right away, you can force a full sync by clicking the "Update All" icon above FeedDemon's subscription list, or by pressing Shift+Ctrl+F5.
Note: Regardless of whether an incremental or full sync is performed, items you mark read, star or tag in FeedDemon are synched with Google Reader every few minutes.