offlineimap-6.5.2.1-1.fc16 has been submitted as an update for Fedora 16.
https://admin.fedoraproject.org/updates/offlineimap-6.5.2.1-1.fc16

I've installed offlineimap-6.5.2.1-1.fc16, and it appears to be working fine, although now it allows me to start two instances of offlineimap simultaneously.  I haven't let them actually synchronize at the same time because I'm not sure that this is intentional.  Is this expected behavior?

(I ought to have said first: thanks for the very quick turnaround!)

If you have multiple accounts, IMO yes, this is intended. If you don't this is probably a bug with the locking (you should get an "could not lock account" error).

Package offlineimap-6.5.2.1-1.fc16:
* should fix your issue,
* was pushed to the Fedora 16 testing repository,
* should be available at your local mirror within two days.
Update it with:
# su -c 'yum update --enablerepo=updates-testing offlineimap-6.5.2.1-1.fc16'
as soon as you are able to.
Please go to the following url:
https://admin.fedoraproject.org/updates/FEDORA-2012-1693/offlineimap-6.5.2.1-1.fc16
then log in and leave karma (feedback).

(In reply to comment #4)
> If you have multiple accounts, IMO yes, this is intended. If you don't this is
> probably a bug with the locking (you should get an "could not lock account"
> error).

Ok, cool; yes, if I let it try to sync an account twice simultaneously I do see the "could not lock account" message.  I used it all day yesterday with no evident problems.  I'll keep an eye on it today and give karma if I don't see any problems.

offlineimap-6.5.2.1-1.fc16 has been pushed to the Fedora 16 stable repository.  If problems still persist, please make note of it in this bug report.