When to automate a repetitive task:

NO-BRAINER: "This is obviously going to be faster to automate than to do it by hand _even once_. Let's automate it right now, and not do it by hand at all."

FORESIGHTED: "Doing it once by hand is faster than automating it, but I'm going to have to do it a lot of times, so it still saves time to automate it first."

NEED A RUN-UP: "I don't yet understand this task well enough to automate it, so I'll do it a few times by hand first to get the idea."

RAN OFF THE RUNWAY: "Great, now I've done this by hand a few times, I think I can automate it reliably! Oh, oops, turned out I only had one more case of it left to do."

TERRIFIED OF RUNNING OFF THE RUNWAY: "This is a one-off, so it would be a waste of time to automate it, I'll just do it manually."
[next day] "Oh, oops, I made a mistake and have to do it again. But it should be fine this time."
[a month later] "Even though I've had to redo it 25 times already, surely _this_ is the last time? So it would still be a waste of time to automate it."

@simontatham
CONFIGURATION MANAGER (Traditional):
I've done this new thing once by hand and recorded what I have done. If I need to do it again I won't have to reinvent the wheel and, oh look, there are some step I can streamline there and maybe if I re-order these operations it will be even faster. And should I get run down by a bus, my replacement will be able to hit the ground running. Also if it seems like we will have to do this regularly I can swiftly automate away all the boring bits.