I have 3 identical brand new Dell 27" S2715H monitors, all running at the exact same recommended resolution 1920 x 1080, 2 of the monitors are attached to DVI on the video card (DVI to HDMI cables) and the third is attached via display port to HDMI active adapter (tried without as well but all the forum say use active), the third identical monitor will not display however if I plug that display port to HDMI into my 46" TV it works fine as a third monitor. I've tried DVI/DVI/HDMI as well, what exactly am I missing here? Attached is the documentation from the AMD website saying this should work, I've even tried different versions of drivers, no dice. I'd like to add that all 3 monitors are brand new, all have been reset to default settings and all have been confirmed working.
Because it works with your TV I don't believe you're doing anything wrong. Although it's ideal to use native connections and cables your setup is fairly normal.
The only thing I can think of is you have a flaky active adapter. Can you replace it? Can you exchange it for a DVI-HDMI active adapter and use native HDMI to HDMI for one of the monitors?
Sorry, that's all I got.