If you're in a standard non-combat (read: less stressful) situation, it's usually assumed that you can "take 20" (if you're familiar with DnD)-- i.e. you automatically succeed to manifest the power.

First, explain to me where you see that assumption in the rules because I haven't seen it.

Second, if you only roll during combat then there are a lot of skills, and a few powers, you will never roll them in combat. I don't believe the intention is that those succeed automatically.

Did you not read the rest of my post?

Succinctly: It's fully up to the GM to decide skill difficulty and circumstances.

Reference: DH1, p184; DH1, p186; DH1, p161; RT p167

In essence, a focus power test failure indicates the psyker was unable to draw the required energy to do it, which may be due to circumstantial events like being repelled by an entity in the warp. (DH1, p161)

The GM decides whether this is the case or not, and how difficult the test would be in the first place. (DH1, p184)

The GM decides whether time is critical, and what happens in the narrative segment of time. (DH1, p186)

As a power example, the telepathy power Reprogram states that a psyker with sufficient time and the malign will to do so may easily succeed at it. (RT, p167)

In other words, if you want to force the player to re-roll the test every literal 5 seconds in narrative time, that's on you.

Deciding that the test is easy, and that he can read surface thoughts by default but must roll to get anything more, is usually more sensible.

You haven't referenced anything from the Beta Test rules.

Now, as a GM, sure I can decide whatever I like with regard to the rules. However, our purpose here is not to discuss what the GM can do with unclear rules or how the GM can decide to handle things when they feel the rules are unclear. We are here to point out when the rules seem unclear to us and how to, perhaps, clarify the Beta Test rules.

You haven't referenced anything from the Beta Test rules.

Now, as a GM, sure I can decide whatever I like with regard to the rules. However, our purpose here is not to discuss what the GM can do with unclear rules or how the GM can decide to handle things when they feel the rules are unclear. We are here to point out when the rules seem unclear to us and how to, perhaps, clarify the Beta Test rules.

How about we do it the opposite way:

Why don't you post the segment of the Beta Test rules that indicates the GM shouldn't decide on the difficulty of tests and what happens if you fail?

I mean, FFG could restate that for each psychic power if you wish. "If you fail your Opposed Willpower test to Mind Probe, your GM should state what that failure causes, and if based upon that you can try again."

In RT, a Mind Probe failure specifically causes a level of fatigue to the psyker, and non-specifically may damage the target and make him aware of the attempt at the GM's discretion.

Of course, some powers can't be used at all on 'unwilling' targets, like Mind Link. (Though again, that's a GM decision.)

Here's what the rulebook has to say:

In some cases, using a test makes the game
less interesting, or allow a chance of failure at a task that should
obviously succeed. The GM should only call for a test when the
results should be interesting regardless of success or failure, and
never for routine tasks performed without pressure.

The results of a test may be simple to determine in some
cases, but there is often room for additional nuance based on
degrees of success or failure. Some tests have obvious possibilities
for how an overwhelmingly positive or negative result might
play out—for example, failing the repairs on a volatile plasma
reactor could cause a dangerous energy build-up and subsequent
explosion...

There's a lot in there about rolls having consequences. So if there is no consequence for failure, don't roll. Do you need literally every little bit like this to be made explicit?

Here's a fun one:

In addition to having a general understanding of a Game
Master’s duties, he should go over specific situations and
systems within the rules to make sure he has a thorough
understanding of how to run a game.

Running a game is an art form, which is a hard thing to codify.

Samples of what may happen when failing an opposed test may help, at the very least to inspire GMs.

Opposed Willpower as in Telepathic Link may be ruled as "his will is just too strong".

A sample decision path following that could be 'you can try again at Push power', or 'wait till you've tortured him a little', or similar.

This is ostensibly my recommendation of 'be aware of what happens should a player fail a skill test'.

I'd say that far from being a mystery, running a game is a social and creative skill, with the goal of creating immersive environments in which everyone can have fun.

So if there's dispute, talk with your players about how they want to play a certain rule, and what might be appropriate for the setting. The rulebook only exists as a guide to help maintain the internal consistency of the world, and to inspire the GM.