[Dovecot] fstat() errors on /srv/mail/<username>/dovecot.index.log

[Zach La Celle]

Dovecot version 2.1.7
Ubuntu 12.04.3 LTS
Kernel 3.2.0-35-generic x86_64

I'm not sure exactly when this started occurring, but sporatically users
report issues receiving email, having email saved to "Sent," etc. 
Looking in dovecot.log, I see the following errors:

2013-10-16 09:53:20 imap-login: Info: Login: user=<user1>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27434, secured,
session=<PnoiBtzoBgB/AAAB>
2013-10-16 09:53:20 imap(user1): Info: Disconnected: Logged out in=93
out=846
2013-10-16 09:53:21 imap(user2): Info: Disconnected: Logged out in=3616
out=495
2013-10-16 09:53:24 imap-login: Info: Login: user=<user3>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27436, secured,
session=<jE5kBtzoBwB/AAAB>
2013-10-16 09:53:24 imap(user3): Info: Disconnected: Logged out in=93
out=819
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:33 imap(user4): Error: fstat() failed with file
/srv/mail/user4/dovecot.index.log: No such file or directory
2013-10-16 09:53:41 imap-login: Info: Login: user=<user3>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27438, secured,
session=<UDJlB9zoCAB/AAAB>
2013-10-16 09:53:41 imap(user3): Info: Disconnected: Logged out in=93
out=819
2013-10-16 09:54:12 imap-login: Info: Login: user=<user1>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27440, secured,
session=<6bI5CdzoCQB/AAAB>
2013-10-16 09:54:12 imap(user1): Info: Disconnected: Logged out in=93
out=846
2013-10-16 09:54:12 imap(user5): Info: Disconnected: Logged out in=736
out=7064
2013-10-16 09:54:15 imap-login: Info: Login: user=<user6>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27442, secured,
session=<t+FnCdzoCgB/AAAB>
2013-10-16 09:54:15 imap(user6): Info: Disconnected: Logged out in=95
out=902
2013-10-16 09:54:20 imap-login: Info: Login: user=<user1>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27444, secured,
session=<c/q1CdzoCwB/AAAB>
2013-10-16 09:54:20 imap(user1): Info: Disconnected: Logged out in=93
out=846
2013-10-16 09:54:24 imap-login: Info: Login: user=<user3>, method=PLAIN,
rip=127.0.0.1, lip=127.0.0.1, mpid=27446, secured,
session=<nOb3CdzoDAB/AAAB>
2013-10-16 09:54:24 imap(user3): Info: Disconnected: Logged out in=93
out=819

These errors are not confined to a single user, and do not occur with
the same frequency.

I originally was running the Dovecot shipped with the default Ubuntu
repositories (don't remember which version, but it was 1.*) and used a
backport to upgrade to 2.1.7 to see if that fixed it.  It did not.

Any ideas why this is happening?