There are a few things to check if your cookies aren’t baking properly. Check your oven temperature with an additional thermometer (a few dollars at walmart) to be sure your oven is holding at the proper temperature when baking, you’ll want to check it at about 10 minute intervals as it’s on say 350 degrees to be sure it doesn’t drop and hold at a lower temp than what is set. Baking sheets, not all baking sheet are the same, thick sheet like in a baker bake evenly without over browning, dark sheet tend to bake fast and dry out cookies easily while thin baking sheets melt the butter fast and result in thin cookies. Use large eggs when baking, a different size will result in a different amount of liquid and alter the recipe, more liquid flatter cookies less liquid firm, less soft, non-spreading of cookies. Be sure to preheat your oven long enough, not so that it just barely reaches the baking temp, then you open the oven and the temp drops. Don’t put more than 1 tray in at a time of cookies, don’t overcrowd the cookie tray. If you need to bake them at a higher temp say 375, place 6 balls of cookie dough and test to see how they come out. Here is a free ebook I created with more cookie tips. https://www.createdby-diane.com/cookie-tips

Yes, if you only have a thin layer of powdered sugar it will melt in the cookie, you need to have a thick layer. You could roll into powdered sugar, then refrigerate until the cookie dough is cold, then try rolling again to get it thicker if you are having trouble with getting a thick layer to stick then bake them.

maybe there wasn’t enough powdered sugar on each cookie, when you roll the cookie dough into the powdered sugar there should be a thick coating of powdered sugar…. like packed on like a snowball, roll it some more the cookie on the tray before being baked you can see it totally white, no brown showing or coming through.

The longer you refrigerate the dough does not make them flatter, just the opposite actually. The colder the dough the longer they will take to flatten. This recipe is different and does not need as long of a refrigeration time, and produced flat cookies time after time. Did you change anything in the recipe?