Well... I have a cronjob that runs every 3 minutes (for a monitoring system).

When the monitoring system stopped receiving data, I logged into the box.

The first thing I tried was to restart cron, in the hope that by simply restarting it, normal cronjob would resume.

That didn't work. cannot start cron; FIFO exists, <date and time>

As you say, cron is "perfect" (I use the term lightly) and it turned out that the problem was with the root password that had expired, at least for running the cronjobs.

export EDITOR=vi fixed the editor.
(Not sure why this would go from vi back to ed, or if it never was vi, why now suddenly it stopped being able to edit cron.)

Now you may say that I should have noticed the root password earlier, when trying to su, but I use a different root account as the box is remotely managed.

I can say this: jlliagre is right. cron is not the problem.

You are not stopped from being able to edit the cron jobs, just a different editor is used and you do not know how to interact with it.
Ed is actually the fallback editor "crontab -e" use when EDITOR is unset.
man crontab is explaining that.

You don't need to restart crond deamon.

Cron need /etc/cron.d/cron.allow with user's list allowed to use this deamon or /etc/cron.d/cron.deny with user's list forbiden to use this deadmon.

If you want to allow all users to use this deamon create a empty file /etc/cron.d/cron.deny