Intriguing error with Git 1.6.3.1: Too many open files

We use Git (1.6.3.1) exclusively here at Box.

Starting this afternoon, we started getting errors when pushing to one of
the repos. It is a very active, bare shared repo, shared among
multiple developers. The
error is:

*"error: unable to open object pack directory: ./objects/pack: Too many
open files"

Things I tried/observed to resolve it:

1) ulimit -H = unlimited, when run as root (original error seems
misleading?). I also killed other proceses that had some open files, and
brought down the total count of open files (roughly lsof | wc -l) to <1000.

2) I can push to several other repos on the same machine just fine

3) git fsck, git gc, git-branch and git-status return the same error

4) I copied the repo (using scp -r, git-clone failed) to a different
machine, but got the same errors when pushing to it

5) I asked #git and the suggestion was that the repo is somehow corrupt and
I should re-push to it

One more thing worth mentioning: Gerrit (code review) uses the same repo
(lots of stuff in refs/changes)

If the repo is indeed not recoverable, I know how to restore it. But I'd
rather fix this if possible. Wondering if it is worth pursuing and what
might be wrong?

Thanks.
-Soham