It sounds as if you need to use an active adapter to enable the third display. To give you some background, please read the below.
The Radeon R9 290 GPUs are all able to output up to 6 displays each with the use of an MST Hub. Your Radeon GPU can physically handle 3 monitors, but this can only be done on cards that feature either DisplayPort or Mini-DisplayPort outputs, but this is only possible when using either a direct DisplayPort-to-DisplayPort connection, or utilizing an active DisplayPort adapter for the 3rd monitors and beyond. Radeon cards can only output two legacy/passive outputs at one time (HDMI/DVI/VGA/passive-adapter-connected monitor).
Utilizing an active adapter instead of a passive adapter utilizes a small chip inside the adapter that converts the DisplayPort signal to a signal that is usable by a DVI/HDMI connection, while still maintaining the DisplayPort standard. Using a passive adapter just converts the DisplayPort output to a legacy/passive output. Active adapters are only available using the DisplayPort output, as there are currently no supported active adapters that use the DVI, VGA or HDMI outputs.
For a list of certified adapters, you can refer to http://support.amd.com/en-us/recommended/eyefinity-adapters, as these are adapters that our certification team has tested with our cards and found them to be compatible with all AMD products. For reference regarding the difference between single-link and dual-link DVI adapters, the single-link has a maximum resolution of 1920x1200, while dual-link adapters (featuring more pins) can support up to 2560x1600. This relies on using a dual-link DVI wire as well, however.
If you are unsure how to determine if your DisplayPort adapter/cable is active or passive, any cable with Mini DisplayPort or DisplayPort on one end, and VGA/DVI/HDMI on the other end will be passive. If the adapter features an additional USB connection, or has the word "ACTIVE" physically imprinted on the adapter, then it will be active, otherwise it is most likely a passive adapter.