Odd. I'm also running ActiveState 5.6.1, and at this moment PPM doesn't find a DBD-MySQL in the AS repository, though there is a DBD-Mysql.zip in http://ppm.activestate.com/PPMPackages/zips/6xx-builds-only/.

You could try downloading the .zip, extracting the .ppd, and installing it via PPM. (The "install" command accepts .ppd files in addition to URLs).

My guess is that this is a temporary hiccup in the AS repository. They happen now and then.