ext3_dx_add_entry: Directory index full!

My log is showing errors like
May  1 05:14:17 corn kernel: [6822807.017625] EXT3-fs warning (device dm-7): ext3_dx_add_entry: Directory index full!

Judging from the minor device numbers in /dev/mapper, that corresponds to my mail spool.

My searches suggest that the problem indicates an individual directory
has too many files in it. There does not seem to be a general shortage
of inodes or space. df -i shows IUse of 11% for that partition and df
says 88% of the ~37G is in use.

First question: what happens in these circumstances?  Are files lost?
Search and indexing are inefficient?  The program trying to write the
file gets an error (it's cyrus. 10 seconds after the errors shown above,
the log has "cyrus/master[8178]: process 11850 exited, status 98".
Usually the status is 0.)?

Second: is there a way to find what directory is causing the problem?

Third: How can I fix this?

I'm running a stock Debian Lenny  2.6.26-2-686 kernel.