Ultrasharp 2001FP no input signal?

I have an Ultrasharp 2001FP Rev A00 dated July 2005 which works fine as long as I don't switch it off - if I do, then when I turn it back on (without switching off the computer) all I get is the Self-test roaming panel with the message 'No input signal' whether it is on D-Sub or DVI. I have to turn the computer off and disconnect/reconnect the cables to get it to function again.

I know it is not an issue with the card (Radeon 9250) since if I plug in any other monitor there is no problem, so it must be the 2001FP.

Is there any way to solve this - I prefer to turn the monitor off when I am away from the computer to save energy.