I'm having the same problem. I bought my Note 10.1 very recently (less than a month ago) from Amazon Germany (I live in Belgium), together with what I assume are the official Samsung USB and SD card adapters (they do sport "Samsung" in big letters on the outside). The adapters however only work the one time after a reboot. This seriousoly blows chunks, as it reduces the perceived usabliity of my tablet (I have a lot of stuff on external hard disks, USB sticks and Sd cards, and rebooting to access it every single time is a major pain in the posterior.
My tablet is totally up-to-date software-wise (Android 4.1.2), it has not been rooted (nor do I have any intention to do this) and outside of installing ES File Manager I have done nothing with its filesystems. I do have a 64 GB sdxd card installed internally, if that might be of any consequence.
I did send an e-mail to the (Belgian) Samsung support center, but the ***** on call insisted that "German software" installed by Amazon Germany is the culprit. There is no "German software" on my tablet; it is a virgin Android install with Samsung's TouchWiz on top.
AFAICS, Samsung botched up the automounter in their latest update (the last time I saw this kind of prehistoric behaviour in a Linux installation, was with a pre-2000 Caldera CD-ROM. There is no hardware issue: my USB connector cable works fine with a pc, the dongles are recognized by Android and USB sticks (with LEDs) even light up, so they should work.