@Lilliputstreasures: Based on the numerous threads about this (and personal experience), the new message banner not going away appears to be only a user interface glitch is not affecting any stats such as Star Seller.
There have, however, been reports about other Message issues that are impacting a shop negatively.
You need to check the applicable CSV file available on your Star Seller page to see which new Message threads Etsy thinks were not answered within 24 hours. When you look at the file remember that that the dates / times are in UTC (not your time zone), only the first message of a new incoming thread is included (all that counts for Star Seller), and usually a new incoming thread is not included until after the 24 hour reply window has passed regardless of when you replied. Star Seller stats (and the CSV file) seem to be updated only once per day so there may be an additional day's delay. There is also a link to the actual message thread so you can verify if the data is correct or not.
