For star seller stats Etsy uses the last 3 months and it's pretty straightforward to see exactly what messages they use for their calculations. Go into your star seller dashboard and the message response time section and download the CSV file. Use this file to see what messages are marked 'no' (ones you didn't respond to within 24 hours). You can move those to spam.
The message that displays in your store ... 'this seller typically responds within a month' are probably based on all your message response times - not just the past 3 months.
If you've ignored spam messages or have totally missed a message - not hard to do - or have only responded to one message in a multi-message thread ... this could throw off your average.
For example, I got a message from Etsy inviting me to be in a test. The messsage said that if I was interested to click on the link and fill out the form. I did. But I did NOT respond to the actual message. That message negatively impacted my message reponse time. It took looking at the CSV file to figure out that was the problem message.
Another example, I used to get multiple messages from the same buyers (before Etsy started combining all messages from the same buyer in a single thread). Typically the buyers were clicking on listings to show me colors/sizes/attributes that they liked. I would respond to just one of their querries. All those messages that I did not respond to negatively affected my message stats.
I hope you can figure out precisely what is affecting your message response message. That should help in a conversation with Etsy and how to protect your stats going forward.
One more thing - if you find messages that you haven't responded to quickly, just mark them as spam. Messages marked as spam are ignored in the stats. It can take a day or two or three for the message stats to update.
Good luck.
