I have a similar setup using xFx HD 5770 graphics card. It is powering three DVI-panels like this :
- Monitor #1 connected through DVI.
- Monitor #2 connected through DVI.
- This display port cable from Dinodirect is connected to the Display port on the card : http://www.dinodirect.com/wholesale-display-port-male-mini-display-port-female-adapter-cable.html. This cable is then connected to the Mini DisplayPort to Dual-Link DVI Adapter from Apple - http://store.apple.com/us/product/MB571Z/A. With a DVI cable the adapter is finally connected to monitor #3.
I have never seen the issue you are reporting, so its hard to offer any solutions. But at the very least check if you are using an active adapter. AMD maintains a list of valid adapters on this page : http://support.amd.com/us/eyefinity/Pages/eyefinity-dongles.aspx.