I have the same issue and I own the Accell Adaptor, my DP monitor goes blank after sitting on the desktop for a couple hours
You're lucky man, mine is at the point that I lose video every 5-10 minutes (just joking about the lucky part, no matter how frequent/infrequent the video drop happens, it's !@#$%^& annoying). I'm sincerely hoping the replacement adapter from Dell does the trick. After looking through this post, it seems the Dell/Bizlink has a higher failure rate...either that or more people bought that version than any other version.
Oh, and for the record. here's my system.
Phenom 9950 Quad Core (O.C.'ed from 2.6ghz to 2.8 ghz) (Cooled by a xigmatek black knight heat 120mm heat pipe setup using arctic silver 5 thermal compound)
Gigabyte MA790X-UD4 Mobo
Corsair 750W PS
4 Gig (2X2Gig) OCZ PC2 8500 Platinum RAM
2 Radeon 5770's
3 Acer H243H monitors (24 inch)
Running ATI CCC 10.6 currently (have had same issue with 10.3, 10.4 and 10.6)
And just for reference sake, 1 WD black (7200 RPM) 500 Gig HD, 1 Samsung (7200 RPM) 1TB HD, and 1 Seagate (5900) 1.5 TB HD
Rockin' Win 7 Ultimate X64