Gumbotron, I know exactly what you are talking about. My loud beep sounds at the same times that yours does, including during logout. It is so loud that I find myself compelled to turn the volume all the way down before I shut down my computer.
Merlwiz79 is correct that it is not it is not an XFCE thing. My laptop had this problem when I used the Mint Main Edition, and also when I used Ubuntu. I have seen a variety of ideas in the Ubuntu forums and elsewhere, even a command line solution, but none of them have completely worked for me