There was a thread a while back describing the exact same issue.
http://en.community.dell.com/support-forums/peripherals/f/3529/t/19434910.aspx
In my case I have a Dell Precision M6600 in a E-Port Plus Advanced Port Replicator. The P2412H is connected via DVI cable.
As soon as my laptop screen goes in standby the external monitor will go in a "Entering power save mode" loop.