It's very hard to get info on this and unfortunately hugely confusing, but AMD cards have a limit on the number of non-displayport monitors you can connect. With older cards (280, 280X), you were limited to two displays via HDMI/DVI/VGA, then the rest needed to be displayport connections. With newer cards (285, 290, 290X) you can have 3 non-displayport connections, but the rest must be DP.
That's why you can have any 3, but not 4 connected, as none of your connections are native DP.
The solution is a simple one, get an "ACTIVE" (must have that word), or "EYEFINITY" DP -> DVI/HDMI adapter. The active adapters function like a native DP connection and will allow you to get 4 displays from that card.