Oops. Thanks for pointing me toward the activity log again. It turns out
that the problem was "IdleTimeOut" after all. I was looking for a server
message with aapproximately the same  timestamp as the client lost
connection message.

dsmsched.log, with the server activity log entry in bold:

11/16/04   02:34:03 Normal File-->     1,048,584,192
/ess36/oracle/BNRD096/bnrd096.fgbtrnd_key_index  ** Unsuccessful **
11/16/04   02:34:03 ANS1114I Waiting for mount of offline media.
11/16/2004 02:49:33  ANR0482W Session 37606 for node VCMR-96.SERVER.RPI.EDU
                      (AIX) terminated - idle for more than 15 minutes.
11/16/04   03:06:57 Retry # 1  Normal File-->     1,048,584,192
/ess36/oracle/BNRD096/bnrd096.fgbtrnd_key_index [Sent]
11/16/04   03:06:57 ANS1809W Session is lost; initializing session reopen
procedure.
11/16/04   03:06:57 Successful incremental backup of '/ess36'

dsmerror.log:

1/16/04   03:06:56 ANS1005E TCP/IP read error on socket = 4, errno = 73, reason
 : 'Connection reset by peer'.
11/16/04   03:06:57 ANS1809W Session is lost; initializing session reopen
proced
ure.
11/16/04   03:06:57 ANS1809W Session is lost; initializing session reopen
proced
ure.
11/16/04   03:07:12 ANS1810E TSM session has been reestablished.

At 08:01 PM 11/16/2004, you wrote:

...
>ANS1809W Session is lost; ...

Chet - This is most commonly caused by preemption, where client scheduling
       is too clumped rather than spread out over the day, and a higher
priority task (e.g., Restore) needs a drive when they are all in use by
lower priority tasks (e.g., Backup).  Check the server Activity Log.

  Richard Sims