I have a mac mini with speakers connected to it using the headphone jack. When I turn off my monitor the speakers disable. I have to unplug the line going to the headphone jack and plug it in again. Then they work. When I turn off the monitor it is acting like I don't have speakers plugged in. The volume icon is grayed out.
If you <option> click your volumebutton (loudspeaker icon in the top bar), do you get a list with different output sources?
When you do, before turning off your monitor, make sure it's set to the correct output, then turn off the monitor.