As per the link above, it didn't require a reboot to get dovecot working again. Dovecot had stopped but after doing this. Reproduced here thanks to the original author on that link, with a "launchctl load xxx" and restarting dovecot, on my Mac OSX 10.14.2 the mail started again. But, I believe that the following will be required.
System Limit (Requires Reboot to Take Effect)
For 10.9 (Mavericks), 10.10 (Yosemite), 10.11 (El Capitan), and 10.12 (Sierra):
You have to create a file at /Library/LaunchDaemons/limit.maxfiles.plist (owner: root:wheel, mode: 0644):
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN"
You should change the numbers according to your needs. They are the "soft limit" (262144) and the is "hard limit" (524288) respectively. For more information, consult the manual page by running man launchd.plist.