Running the newest version of the alpha (v1.4.0 alpha5) is actually stable. Seems to be running fine on my machine now. Would you recommend continuing to run the alpha? I've got 10 of these babies and a 7950 hashing away.
EDIT: Though, I am getting errors such as:
2013.06.14 [03:19] Icarus (COM36) ERROR: Icarus (COM36) ran out of work. Idling...
If it works ok it will become the next beta, and hopefully soon the final 1.4.0.
Hmm, is the status line at the bottom showing zero queued work at the time? (grey boxes)