This is very likely a kernel problem: https://bugs.launchpad.net/ubuntu/+source/linux/+bug/986845
Slackware 14 is using 3.2.28.
As nobody is reporting eject problems, I don't expect much help from the Slackware community because Trinity is not an officially supported desktop. Xfce 4.10 and KDE 4.8.5 are officially supported and eject works fine with both.
Darrell