Most likely, GPU/driver related, possibly software.
I have a 7970 and 5770 installed currently, and when it happens, it only appears as a dotted line on the monitor connected to the 7970, when I move it to the other monitors connected to the 5770, it appears normal. Did the same thing when I had a 6670 installed along with the 7970.
For me, it was caused primarily by the flimsiness of the Gigabyte pcb/weight of the heatsink bending the board and mostly only happened when the card started artifacting - tying the card to the case to remove the bend improved the artifacting greatly. The other thing that caused it for me, was hardware acceleration in Firefox, disabling that eliminated it completely for the most part; it has only happened once in the past ~4 months.