Try running it on one GPU and see if the issues persist.

You can also check and see what background programs are running (Ctrl,Alt,Del)

Thanks for the suggestion. I tried disabling SLI and it still crashes.

cleaned out cooling vents/fans anytime?  with mine and dual 7970's I clean em every 2-3 weeks now being summer

Thanks for the responses guys. After a few days of use after my complete driver reinstall, the only times the graphics have crashed again is after a few hours of intensive gaming. This seems to indicate that overheating may be the actual problem. I went ahead and cleaned out my gpu fans last night, they were a little bit dusty. My friend suggested re-pasting them. Does the thermal paste they use during assembly wear out quickly and should it need to be replaced after less than two years?

well usually  thermal paste last long but they use a thermal pad and  in some cases wasn't installed correctly ,  I use arctic silver , I run dual 7970's and rarely get over 70C  same with my 3940XM cpu rarely hits more then 65~ C ..... ambient of 20C

I also experienced this and still having the same issue after they replaced the hardware. From the reading of this thread, it seems to me proper cleaning of fan/cooling and proper install of thermal paste will resolve this expensive replacement from Dell.

Definitely sounds like an issue with the hardware.
I'd try and test out the cards individually (if possible and with SLI Disabled). See which one of them is failing. Try running a Video Benchmark to see if it crashes while you are doing so.

Also, if you can check if it is happening with another game aside from Star Wars: The Old Republic it would help out a lot to see if it is an isolated problem.

Keep me posted!

I haven't played SWTOR in about 2 months now, and my graphics cards have not failed at all during those two months. I have been playing other games such as Watch_Dogs, Archeage, Diablo 3 and others with no graphics card failure. It might have just been the amount of time I would play in one session combined with the rather high graphical processing amount done by SWTOR that was just overheating my graphics cards after a while. The last time I did play, I was able to play for several hours before the failure occurs, but once it occurs, I have to leave my laptop alone for a while to cool off before I can do anything graphically intensive. I went in and cleaned all the fans, I have not re-pasted the cards or anything.

Mine failed just from normal usage. Tried disable SLI still having the same issue; successfully recovered from graphic card, then later failed to recover and hang computer or restart itself. Then, I switched to integrated graphic card no problem ever since.

Well, from what you're telling me, it points out that those crashes seem to be more related with Start Wars the Old Republic. Diablo 3, Watch_Dogs and I believe even Archeage are a little bit more graphically demanding that SWTOR.
Try running any of those for the exact same amount of time. I believe you will have different results than just playing SWTOR.

Keep me posted though!