The problem seems to affect many android tablets which address the (inserted) sdcard with /mnt/sdcard2.
If I understand correctly, this behaviour is by design unless a manufacturer decides to circumvent it (which toshiba does not).
People in other forums wrote that writing with 3rd party apps would be possible when the SD card is formatted with the file system exFAT (which can I.e. be done in Windows 7).
I did not try it out yet though.
Sources:
http://forums.toshiba.com/t5/Excite-Tablets/SDCARD2-not-writeable/td-p/313476
http://www.thriveforums.org/forum/toshiba-thrive-development/12995-at300-101-ice-4-0-3-rooting-possible.html
If you decide to try it out It would be nice if you could give feedback here whether this worked or not.