Is this a firmware or driver problem,
or am I doomed to having only two 1080 outputs from the ATI card?
No,
and No.
This is a problem based on AMD/ATI decisions based on the POWER available to converter/adapters. There isn't enough for three displays immediately, but there are solutions.
The first connector is a Dual-Link capable DVI-I, which has direct Dual-Link DVI _OR_ direct VGA (in the bar and the four pins around it at one end of the connector. It also picks up the top last pin off the grid array to complete the set of five signals for VGA: Red, Green, Blue, H-Sync, and V-Sync, (with the bar as the common return for all).
Those two little connectors are Mini DisplayPort, which are plug or cable adaptable to DisplayPort without conversion. They can also be coaxed to produce a signal that is DVI-compatible in timing, but not always powerful enough. To run three displays, each adapter needs the Re-Driver circuitry found only in Adapter/Converters sold as ACTIVE (read: POWERED) Adapters. There is a power lead in the interface that suffices for Single-Link DVI. For Dual-Link DVI Apple has chosen to use an additional USB lead to pick up more power still. If present, it MUST be plugged in!
ATI/AMD has an article on this subject, and has tested several adapters. Read the accompanying table Very carefully, as ACTIVE and not-active adapters are listed, as well as Displayport and Mini DisplayPort. The most common Accell ACTIVE adapters are available on Amazon, but Amazon search is imprecise by design to include more items than you would get from an exact search. So Again, Read Carefully!
http://support.amd.com/us/eyefinity/Pages/eyefinity-dongles.aspx
Dual-Link DVI is so-called because the data signals in the connectors and cables are doubled, to accommodate displays wider than 1920 wide.
To get HDMI, a DVI -> HDMI cable that swaps the wires around is all that is needed.