I wonder if what's happening is that these personal computers are
gaining their network access via DHCP, wherein their network identity
is dynamic and can change upon renegotiation, as when the dormant
computer is awakened after some time.  As I understand TSM client
password encryption (per IBM Technote 1224568 et al), it is keyed to
the TSM client nodename; and, as the Nodename option doc says, where
no Nodename is set, the hostname determines the client identity for a
TSM session; and where the hostname changes with network position,
you have problems.  Thus, I wonder if these Macs lack a definite
Nodename defined in their client options (/Library/Preferences/Tivoli
Storage Manager/TSM System Preferences)?

It may well be more complex than that, but this is one area to inspect.

   Richard Sims   http://people.bu.edu/rbs