I notice my trashdir is excessively large for our small installation. When I went to try the trick to immediately clean the file, using the instructions in https://moodle.org/mod/forum/discuss.php?d=191275, I found the record fileslastcleanup gives 26 Nov. 2012 as the last time it ran.
This matches the last date automatic course updates worked.
I guess this is a cron issue, but I can't work out where the problem lies. Cron runs fine from the browser. My cron command is:
/usr/bin/curl -s https://mysite/admin/cron.php> /dev/null 2>&1