Just thought I'd add to this thread as I am yet another person experiencing this.
My card constantly unmounts/re-mounts if I try to take or browse through photos. Due to the fact that the internal memory is in such shortage, I really depend on being able to utilize my 64gb sd card. This got especially frustrating due to the fact that I've been traveling a lot and have wanted to take lots of pictures, but am constantly having to deal with the phone saying the sd card has been removed.
I tried formatting the card, then tried several other cards (kingston 16gb, sandisk 32gb) and all had the same issue. Finally tried a factory reset on the phone and not even that did the trick. I got fed up and took it to T-Mobile to do a warranty exchange, but they would not honor the warranty! They hooked the phone up to some Samsung diagnostic software that reported that my phone was in good health, and of course the issue would not repro in front of the T-Mobile rep.
So in my desperation I rooted the phone and put the Google Play Edition ROM on there. This completely cleared up the SD card issues. Not once since switching to the GPE ROM have I experienced the card unmount unexpectedly (almost 2 months now).
This issue seems to be purely with Samsung's buggy software. Today, after using GPE rom on my phone for almost 2 months, I decided I missed the Samsung camera app enough to give the stock software another try. Right after switching back to Samsung's stock software the issue IMMEDIATELY returned.
Samsung...update your crappy software!