I published my book on June 11, 2017, its enrolled in KDP Select and I haven't changed the price in over a month. I cannot figure out why its still not eligible for a count-down deal. The link "Why" just gives general reasons why, not why mine isn't specifically.
There are a few other caveats, as well. E.g., I don't think you can do a countdown deal unless your price has been unchanged for at least 30 days. And, IIRC, there are some problems with trying to do either a countdown or free day (or both) if it's too near the Kay Yu renewal date. So I'd suggest a close re-reading of the Kay Yu promotion specs.