Hi,
I just wanted to post my information here for others to see. I had a HIS 5770 with my 3rd monitor running on a Dell Active DisplayPort to DVI - see here
http://www.scan.co.uk/products/dell-bizlink-active-displayport-to-dvi-%28dual-link%29-adapter-1080p-ready
It worked for a while at first but then I started to lose the DP connected 3rd screen as many others here have too.
I live with it for a while and eventually decided i either replace my 5770 or get one of these
http://www.tweaktown.com/reviews/3468/quick_review_sapphire_radeon_hd_5770_flex_1gb/index.html this card would give me 3 screens without the need for the active adapter and I'd get crossfire too. So i figured it was worth a go. I didn't get the retail pack in the review above i got an OEM version from pixmania (i didnt know i was getting this, but whatever). The bundle i got didn't come with the HDMI to DVI adapter, so i thought i was screwed. I said i'll set it up andway and can get the adapter myself.
Ok so the interesting bit. On the new card I used the same Dell Active DisplayPort to DVI for the time being and it didnt drop the DP connected monitor at all. Screen was up for over 16 hours yesterday. So it wasn't the adapter in my case (or at least the adapter works now with a different card). I'll update this post if I have any change.