In thinking more about this problem...

If the TSM client was causing all the virtual storage in your system to be
exhausted, there would be major, obvious manifestations in the system.
In the case of AIX, it would issue SIGDANGER signals to all processes warning
of impending virtual storage exhaustion such that they could end gracefully
before AIX was forced to do SIGKILLs to contend with the problem.  If Unix did
have to kill off processes, this would be evident in your Unix process
accounting records (check there).  In addition, your AIX Error Log (errpt)
should contain PGSP_KILL entries around the time of the problem.  If this was
not in evidence, then it suggests that it was the case that your process
exceeded its Unix Limits value for memory utilization.

From the same set-up in which a backup would be done, do 'ulimit -a' to see
what your process limits are.  In AIX, also check /etc/security/limits
definitions and make sure that root's memory utilization is not artificially
constrained.

   Richard Sims, BU