Logs are only backed up once and, as you have discovered, there is no way
within ADSM (or within Informix, for that matter) to gracefully age them
away.  One user wrote a script to eliminate them from Informix and another
user has written a C program to eliminate API-backed files (which logs are)
from ADSM.  And that's what it currently takes to 'clean up' these logs.