So why do they keep asking?

Question

Settle down.   We are all understandably upset — once again — but this meeting is called to order.

                 [Weary communal s  i  g  h.]

Now that we have recited our non-denominational invocation we may proceed with this week’s award for most answers.   And it goes to...

              ...you!

Yes, during your day job you answered question after question from a procession of distraught “visitors” (so-called out of consideration) about recommendations for what to do, along with some rather probing questions about your fellow employees.

And during your off hours loitering with others of us, you answered ever more desperate questions from lost souls about where to go, among sneaky attempts to reveal your friends’ personal habits.

All the while, you knew your answers would be met with suspicion, as are all of ours, which is why we lament, yet you nonetheless responded as best you could.

To be fair, of course, you and I must admit to distrusting most of us as well.

With that, I call to a close this meeting of ________________________________.
                      (What puzzle “pieces”?)

Free hint, meant to seem confusing:   Are you even sure you won the award?

Answer 1

"We" are

Knights and Knaves -- habitual truth-tellers and liars -- from Smullyan-style logic problems. And perhaps also "Knormals" who don't always tell the truth or always lie.

... We are all understandably upset ...

Perhaps (as mentioned later in the speech) just because no one ever trusts us. Or perhaps because of the tragic recent death of Raymond Smullyan, who gave us so much productive employment and so many interesting conversations.

... during your day job ...

As a guard at a curiously designed prison with indistinguishable doors leading to the cells and out to freedom.

... "visitors" (so-called out of consideration) ...

It wouldn't be polite to call them condemned criminals.

... recommendations for what to do ...

Which door should I go through?

... rather probing questions about your fellow employees ...

If I were to ask him what you would say if I asked which door to go through, what would he say?

... your off hours loitering with others of us ...

By a junction in a road. Apparently one branch leads somewhere nice and the other branch somewhere not so nice.

... sneaky attempts to reveal your friends’ personal habits ...

Is the other person standing here a liar?

... distrusting most of us ...

I took this to be because in these puzzles one can't always tell what a given other person is, so we'd have to distrust almost everyone. But there's another explanation, which OP has indicated was intended: if we have knights, knaves and knormals in something like equal proportions, then "most of us" are not perfectly trustworthy.

... puzzle "pieces" ...

As Duncan observes in comments, knights are chess pieces.

Are you even sure you won the award?

Well, is the guy making the announcements a Knight or a Knave? Usually, though, we're assumed to know one another's knature. But if the writer is, or might be, a knormal rather than a knight or a knave, we can't tell even if we do know that.

Answer to question in title ("So why do they keep asking?"):

Well, they want to know how to get out of prison. Or which door has all the gold behind it. Or which path leads to the village serving free beer. Or how to get to heaven rather than hell. Truly, ours are weighty responsibilities.