Hello, do you have AlienRespawn installed?

If you do, do you remember if it has updated recently?

If you do have it and it has updated there is a small chance this may be causing issues, I've had a few problems recently with my customers reporting issues with their laptops not recognizing the dedicated GPU'S, so far I have been able to resolve this issue with uninstalling AlienRespawn.

If this does not work the Melina is correct, you probably have a faulty GPU or perhaps motherboard.

If the video card is not been recognize in the BIOS then yes it might be failing and the best solution will be to get a new one.

If you are still under warranty send me a PM with your service tag and a brief description of the problem so I can help you further. 

So i was able to get the bios to see the gpu by tearing down the laptop again, and cleaning the gold contacts of the gpu with cotton tips and isopropyl alcohol. I saw your post and decided to (for some stupid reason I guess) update AlienRespawn. It made my computer reboot and get a apc index mismatch bsod. I booted back up again and bios did not detect my gpu. I promptly uninstalled AlienRespawn and rebooted to the bios and saw that it detected my gpu once again. I am not sure what is going on exactly.

i think is a OC problem or maybe a undervolt problem... maybe you are playing with the stock specs of your gpu and when the laptop detect an error the gpu will be unread by the motherboard, so thats why you have to reinstall the BIOS and etc etc etc... 

make sure that your gpu temperatures are normal, when your gpu reach the max temperature,you have a bluescreen and a reboot sudenly. and the gpu will be unread in some cases. 

if your problem is the second please make a re-paste, is easy and use a good paste like IC diamond 7. and change the thermal pads if you can. dont use cheap paste , like conductive paste, this can  be your problem too 

make a test with dell support assist application ... your gpu or motherboard is dying

I am not OC or messing with the specs at all. Everything is stock specs, as was from the factory. GPU isn't heating up at all.

The Dell Support Assist Application test passed on everything, including gpu.

mmmm strange ... as i told you before ... i am thinking that your problem is a voltage problem ... i am thinking is impossible to test your charger ... some of your friends have a similar charger as you ? can you try with another power supply ... you maybe have a 150W charger without use.

i tell you this, because i had another alienware ( M14X) and i update to a unlocked BIOS and i cant see it but it has a little change in the volt, like 1.1V and not 1V like default. when i fully charge my gpu while gaming my laptop shut up and restart .... in the next restart my pc doesn't show the nvidia gpu, and i have to re install the Bios to fix the problem... maybe you have a mod BIOS or you charger have a little problem..

i hope it help you, have a nice day :)