Here is a small blurb of what the log shows:
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: requested www.abms.benelogic.com/
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: client requested www.abms.benelogic.com, updating to memberp06.benelogic.com
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: rewriting URI to /AAEP/
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: requested www.abms.benelogic.com/Benelogic/PF/Templates/BeneBlue/images/logo.gif
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: client requested www.abms.benelogic.com, updating to memberp06.benelogic.com
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: rewriting URI to /AAEP/Benelogic/PF/Templates/BeneBlue/images/logo.gif
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: requested www.abms.benelogic.com/Benelogic/PF/Templates/BeneBlue/images/help_disabled.gif
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: client requested www.abms.benelogic.com, updating to memberp06.benelogic.com
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: rewriting URI to /AAEP/Benelogic/PF/Templates/BeneBlue/images/help_disabled.gif
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: requested www.abms.benelogic.com/Benelogic/PF/Templates/BeneBlue/images/signout_disabled.gif
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: client requested www.abms.benelogic.com, updating to memberp06.benelogic.com
Dec 5 14:08:49 tmm tmm[673]: Rule AAEP_Redirect : Client 172.29.2.100: rewriting URI to /AAEP/Benelogic/PF/Templates/BeneBlue/images/signout_disabled.gif
Appears to be doing what it should. So maybe I need to look elsewhere within the LTM for the issue? One thing I forgot to mention (which may be critical) is that we're running in HA mode.