From my experience, there isn’t one magic “cheapest day” to buy United flights, but I’ve personally had the best luck checking prices mid-week, especially Tuesdays and Wednesdays. Last year, I watched a fare for days and noticed it dipped slightly on a Tuesday morning, which saved me a decent amount. When I later needed to change the return date due to work, calling 877-297-0699 was honestly the easiest way to instantly book, cancel, or modify my United flight without dealing with online glitches.