I crash to desktop literally randomly. It can be 2 minutes after I load a character for the first time. It can be 2 hours after playing that character after a crash. It happens in taxi's, walking on ANY planet outside, inside, underground, upside down. I have had it happen in combat, while talking in conversations, as well as checking my mailbox. I have had this happen in Flashpoints (4-5 crashes in one run of the Esseles alone with a level 40 rushing me through it...). I've had it happen while sitting on the john flying from point A to point B on my ship (of any flavor).
There is no trigger, no replication, that I can tell. It is 100% random. This problem has plagued me since launch and my playing time has dropped quite considerably.
I just gave up trying tonight after crashing for the 4th time on a low level Imperial after playing for 3 hours (and then rebooting) on the Rebel side of things.