One thing that might be worth a try is to use the web interface to the 3584
to switch the locations of one tape that is consistently unavailable with
one that is consistently available.  Run another 'audit library' to update
TSM, and do a 'q libvol' to get the home cells for those two tapes and
compare with the 3584 page to make sure everything is in sync.  Then try to
do moves on each.  If the same tape goes unavailable and the other does not,
that would tie the problem to the tape in some way; if the reverse happens,
then it could be a cell/accessor alignment issue.  If both or neither go
unavailable, then I have no idea.

Out of curiosity, what are the activity log messages given when the tape is
marked unavailable?