M18x R2 Graphics Crash doesn't seem to be a software problem.

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

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!

Yesterday I had more free time than usual, so I decided to play archeage all day. After 8 consecutive hours of playing archeage, my graphics cards crashed. Since then, I haven't been able to play more than 2 consecutive hours. Do the 675m cards have an issue with retaining heat? It takes a long time to build up enough for them to shut off, but once they are hot, they stay like that for a long time. Last time they overheated like this (from playing SWTOR for an extended period) it took one or two weeks before they went back to "normal." Again, I am assuming the problem is overheating, since doing nothing graphically intensive for a while seems to abate the symptoms.

I found this today:

http://en.community.dell.com/owners-club/alienware/f/3746/t/19545021?pi21932=1

It documents a similar issue (although the people in the thread get less play time than I do before crash). I checked my bsod analysis and they are the same bsod errors in the nvidia drivers. Given that the thread is 22 pages over 9 months and their ultimate solution was to upgrade from the 675m to something newer, it doesn't look promising.

Ok, it got worse. After starting up today I literally cannot play anything for more than 30 seconds before black screen. I tried with SLI, causes black screen freeze and buzzing noise (audio freeze). Tried disabling SLI and that causes black screen, but audio keeps playing. Wanted to switch to integrated graphics so I could at least play on lowest graphics without crashing, but for whatever reason, I have no integrated graphics driver installed. I went to dell's driver download center and got the intel hd graphics driver for my cpu model and it said I don't meet system reqs when I tried to install. Went to intels website to get the driver for my cpu. Same message. Tried to get dell's driver tuner or whatever to automatically detect and install drivers. It fails during the scan every time and completely does not work. So as it stands, after 2 months of being fine, I suddenly cannot play pc games at all. At this point, my plans to build a desktop are now a priority because I have no machine to play pc games on. At this point, I don't think it is overheating, I think the 675m card just has an inherent defect that gets stressed over time until complete failure. I guess I just picked the wrong card.

Given that you're still going through this issue. Go ahead and send me a PM with your service tag and a thread to this post so I can check for other options.

Sorry, Glithir that happened to you as well. I am having exact same problem AGAIN, but I am able to switch to integrated graphic driver by downloading Dell's Alienware On Screen Display Application. I hope it is stable enough to let you install the app so you can press fn+F7 to switch to integrated graphic card.