There is an apar "fixed" in ADSM v.3.1.2.55 for this.  I don't know about TSM 
3.7.

Try the expire inventory fixdir=yes, if that moves it along, then you have the 
same problem I do.  What I do, is run the expire daily with the skipdir=yes 
option, then go back and run it without the fixdir=yes option the rest of the 
day.  You can check the actlog for msg=4391 to see which nodes/filespace/type 
is the culprit.

The molasses effect is due to "duplicate" directories from archives and the way 
the expiration process checks for files below before deleting the parent 
directories.

I have changed by archives to use explicit descriptions like "week1", "week2", 
etc to prevent proliferation of archive directories (with date/time stamped 
default descriptions.)

From the 55 ptf readme:

IY06778 MULTITHREADED EXPIRATION RUNS VERY SLOWLY, BITFILES EXAMINED
        INCREMENT VERY SLOWLY

 The expiration algorithm has been altered to improve
 it's performance while expiring archive files and directories.

 In addition, a new parameter has been added to the
 "EXPIRE INVENTORY" command.  The parameter is "SKIPDIRS".
 The minimum abbreviation is the first two letters of the parameter
 or just "SK".
 The  parameter accepts either a "YES" or "NO" for the  value.
 So, to specify this parameter on the
 "EXPIRE INVENTORY" command, examples are:

 "EXPIRE INVENTORY SKIPDIRS=YES"  In this case,
 expiration would run and for any DIRECTORY type objects
 stored on the server, expiration would skip those objects.
 So, even if the directory was eligible to be expired based
 upon the policy criteria, the object would be skipped because
 this parameter was specified.

 "EXPIRE INVENTORY SKIPDIRS=NO"  In this case, expiration
 will process as it does today - it will expire any
 possible files or directories based upon the appropriate
 policy restraints.

 By allowing expiration to skip directories this will help
 customers to keep reclamation processing working.  Typically,
 the file objects are likely to be taking up space on
 sequential media (where this is the storage pool configuration
 that a customer is using.).  By allowing expiration to
 expire the file objects, we free up more of the sequential
 media space and allow reclamation to continue having tapes
 to reclaim.
--
Richard
Richard