This six year old Tom's Hardware Forum about the same issue you are having on the HD 6970 (you didn't specify which model of HD 69xx your have) explains why you can't see three monitors if one is connected via HDMI: Have the 6970 & three monitors... how to get all three working? - Displays .
This is OPS initial Post:
I've been running dual monitors off my MSI 6970 for a while now (both Asus VW246) with one connected to the HDMI port and one using the DVI to HDMI adapter that came with the card.
Since I had an extra DVI port I ordered a third identical monitor only to find out that one of the DVI ports is shared with the HDMI; in other words, you can't run three monitors using the HDMI and both DVI ports.
I know I need an adapter from one of the two (displayport?) connections on the card but I'm confused with this 'active' and 'passive' adapters as I'm not sure which I need.
I've also seen most all the adapters available on Newegg have bad reviews... are there any known good brands?