OEM recovery needed: sysman user exists, but OEM directory does not. Cannot drop repository, and c

Apologies if this is similar to an earlier post, but I really, really do NOT want to have to recover an outdated backupset to fix this.

Oracle 11.2.0.1, with terminal patch in place, on Windows 2008R2

Observations:

(1) OEM was setting the SYSMAN user account to "locked(timed)" several seconds after I unlocked the account.  When I shut down OEM (with emctl), the SYSMAN account remained "open".

Question: What would make OEM lock the SYSMAN account like that?

(2) The OEM page became inaccessible (probably because the SYSMAN account was locked)

(3) The database and OEM were doing fine a couple of weeks ago, and then the flashback_recovery_area ran out of space, and things backed up from there.  I added space to the flashback_recovery_area, did a successful full backup of the database, and proceeded to attempt to fix OEM.