I haven't tried, but in the "Sorting Office/Filters" for that account, you could create a filter in the "read messages" or "replied messages" category with the condition "AGE >= 10 DAYS" and action "Move to the folder \\MY_ACCOUNT\MY_ARCHIVE".
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As Daniel said, the sorting off/filters filter may work. I say may because a few years ago I tried it but I have in the back of my mind that there were issues with it. One I think is that it wasn't automatic, but I'm not sure. I say that suggesting you make sure you back up and also that you test on several folders. I also assume you're using POP.