I think this answer is incorrect. I have all days filled with at least 3 caches. One Date, Dec 16, has only 3 caches found and I have been awarded a "3" add-on. I checked and I had found 1 cache on each of 3 different years. When I do a search for Loop 4 only Dec 16 is shown as being needed.
BUT...
On Dec 25, I have found 6 caches - 1 in 2009, 1 in 2012, and 4 in 2019. IF this Badge was actually checking Days cached with logged finds, Dec 25 should be required for Loop 4. Dec 25 is not required until I check for Loop 7.
Therefore, the badge is not checking for days cached, it is checking for total Number of caches found on any given day of the year. If you find 10 caches on April 1 of one year and never find another on that date in any other year. It won't say you need another find on April 1 until you search for Loop 11.
You could not have an Add-on higher than 5 because there have only been 5 Leap Days since May, 2000.