I was able to get things re-running not by downgrading, but by manually restarting each zarafa service in /etc/init.d.
Upgrading to zentyal-core 3.3.7 from 3.3.5 introduced a fatal exception in Zarafa - the object method enableInnoDBIfNeeded is now missing.
I'm highly concerned that this class of bugs would exist in releases of software supposedly destined for enterprise use.
My /var/log is filled with hundreds of megabytes of Zentyal exceptions all the time. Surely there could be better bench testing for Zentyal.
The problems in Zentyal are non-trivial. In the past three months, going to 3.x has caused the following utterly weird and fatal problems: database corruption, user mailboxes randomly unlinked and deleted, core dumps due to integration of non-functional versions of third-party components, dovecot integration with zarafa dying mysteriously once per week and requiring a system reboot once per week, zentyal keeling over when imap sync is stressed...
I have been using Zentyal for the past few months to test its worthiness as an enterprise mail/groupware server. The problems I've seen make this solution seem quite immature; I like what the company is trying to achieve, but at this time, I couldn't possibly recommend this solution to anyone that needs to count on their email.