My Canon 60D does not save photos to the SD card when I take photos while using the swivel screen/viewer. It happens with different SD cards, so I don't think it is caused by a defective SD card.
My best guess is that you are using quick focus and it isn't actually taking the photos. When you are using live view with quick focus, the mirror will engage to redirect the image path to the PDAF sensor. It will then focus and take the image and then the mirror will go back in to hiding. This ends up making a bit of an odd pattern of sounds and it is easy to think that it is done taking an image when it is actually just starting.
I actually had this occur while shooting on my 5D Mark iii in live view during my sister's wedding and we had to rely on the professional photographer that was covering it officially for images because none of mine actually took, despite sounding like they had. (Up to that point, I had never used LiveView due to the lag issues and preferring the view finder.)