Nice idea. I haven't come across an extension that does that. It's a pretty small sized development project in my opinion that could be achieved through a few new attributes.
You could go down the route of a timed message with a from and to date. This would need three new product attributes "Product Message/Note", "Product Message From Date", "Product Message To Date". A small extension as part of your site can then just check those dates and show the message if between those dates, similar to how the special price functionality works. Note that if you have a full page cache mechanism, you will probably need to make sure that this gets flushed at the start of each day so that the message is added/removed if need be.
Alternatively, you can have a custom out of stock message without a date. This is a message, again, through a new product attribute which is shown when the product is out of stock. Instead of relying on the additional date logic, you could simply make sure that this is only shown when out of stock. It would then automatically be hidden once you update the product stock levels.
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