Afterwards, I realized that only our Galaxy S3 and Asus Nexus 7 testers were complaining.
I found this bug issue on Android's bug tracker and it sounds quite similar to what is happening to me:
code.google.com/p/android/issues/detail?id=39002 (can't post link yet as a newbie, but kindly check it out)
This sounds like a serious architecture problem which effects all Internal SD cards devices.
These devices are limited to 1024 file descriptors only!
Can anybody confirm this problem?