[Dovecot] Can't start dovecot from heartbeat

I get the following error:

Fatal: epoll_create(): Too many open files (you may need to increase /proc/sys/fs/epoll/max_user_instances)

Works fine if I start it by hand, I'm guessing it has to due with the environment heart starts it in?

My first thought was to do exactly what the message suggests, but my kernel doesn't appear to define max_user_instances, but there is a max_user_watches.

I'm running 1.2.8, by the way. But I had a similar problem with earlier version too.

John