Guys,
I had the exact same problem. I am using a Sandisk Ultra Class 10 32GB mSD card (loaded with pictures, music, videos, books etc, with only 4GB free space), purchased in Nov-2012. Before I upgraded to this, I was using a Sandisk Class 4 32GB card without any problems since I bought my S3 in Jul-2012.
For the past couple of months, whenever I press the power key, I will see the notification "SD card not found", then immediately, the card is found and everything works as usual.
Then, suddenly yesterday, I got the message "SD card corrupted, reformat?"
Of course I chose 'NO", then I re-booted the phone, and everything works.
This afternoon, the same "SD card corrupted, reformat?" came up and after I chose No, it automatically dismounted my card. Since then, The card cannot be read by my S3, even after I reboot. BUT, when I plug it into my PC, it works.
I started to search the forums and found that a lot of people has the same problem.
==> I just managed to get it to work!
I am not sure if this is the solution, but, after checking the forums, a lot of people are recommending that I format the card to FAT32. So, I backed-up my card, then, on a whim, decided to delete some videos until I have about 7GB free space, and plug it into my S3.
The card was recognized and seems to be working now. When I press the Power key, I no longer the the "SD card not found" message!!
Can it be that if we load the card above a certain amount of space, the S3 starts getting problems with recognizing the card?
Anyway, for the past hour, the card seems to be working fine and my S3 recognizes my Class 10 32GB Sandisk card. Will try for a couple more days and if it still works fine, then, this may be a temporary solution.
Let's see.. Will keep you posted.