The public release of 1.06 beta isn't in the FTP area. It's in the Extras section and I found the problem. Somehow the CHMOD for a couple of the files necessary for the download counter to function got changed. It's fixed now. Not sure how that happened though.
Edit 1: Turns out the hosting service moved my domain to another server due to the high volume of traffic my site gets. During the move some of the settings (passwords, CHMOD, etc.) didn't get transferred right. It's all fixed now.