Why must the Avalon be perpetually in autopilot?

The entire point is that the Avalon is not the first or second homestead trip. It's a routine trip after the success of Homestead 1. Considering the time span of this trip, and the first planet is taking in trillions of dollars for the Homestead Corporation, both the hibernation pods and space ships are proven technology. Homestead Corp isn't even the only company doing this.

The plot revolves around a one in a trillion accident where the Avalons shields are overwhelmed by multiple small strikes then a very large asteroid, which struck the only non-redundant critical system, which is then overwhelmed by systems being online for longer than expected. The system can normally self repair, which Jim, Aurora and Mac all state is how the system should work. With Jim awake, everything starts failing slowly, not at once.

Had that freak accident not happened, there would be absolutely no need for a caretaker like Mac to be up at all. The system would work like it should and everyone profits.

Consider that Homestead is a for profit company which we are told constantly, They would calculate that the freak accident is too small to worry about in a cost benefit analysis, and that paying the employees for 120 years of work, as well as 120 years of supplies would hurt their bottom line.

Bottom line, profit is king, unnecessary expenses will be cut and outlier issues with low probability can be ignored.

Does the movie or its crew address this possibility?

No they do not.

It is a pretty common theme through out the movie that the ship is built with the assumption that malfunctions, errors, failures, etc. can not and do not occur. Consider the scene when Jim Preston wakes up and is trying to get information from the computer about what to do in case of a hibernation-pod failure.

Jim: What do I do if my hibernation pod malfunctions?

Computer: Hibernation pods are fail-safe. They never malfunction.

Jim: Well, I woke up early.

Computer: Can't happen.

Jim: How long until we get to Homestead II?

Computer: About 90 years or so.

Jim: And when are all the passengers supposed to wake up?

Computer: Not till the last four months.

Jim: How is it that I'm sitting here with you with 90 years to go?

Computer: It's not possible for you to be here.

The humans/engineers, etc who designed and built the ship did not anticipate the possibility of a failure occurring as evidenced by the computer's responses.

This is a fairly common theme for science fiction movies of this type, typically used as a way to demonstrate exactly what you mention, which is that humans are better at reacting to unforeseen events than artificial intelligence is and we should not be so quick to trust machines to take over for people.

According to a deleted scene, all previous interstellar trips of the Avalon have been without incident, meaning a human pilot is unnecessary

In this deleted scene, Gus indicates that the Avalon has made trips before and they have all been without any sort of serious incident.

The Avalon's made five interstellar trips, I've made all five of them. I've never seen anything more serious than a burnt piece of toast, and now this…

Given the Avalon's track record, it's not really worth the hassle of waking up crew members in a rotation if there is nothing for them to do. And of course, keeping career crew members like Gus awake and out of a hibernation pod means that they have a shorter lifespan and fewer opportunities to run future ships (although it seems that the crew were not going to be returning on the Avalon, since Aurora would be the first person to return from a colony world).