from what I have read here in the comments, it seems the final -s comes in place of -r where there can be a "hverandre" (each other) implicit. So here the meaning might be "why are they failing each other?". You can also choose to use the -r termination AND the "hverandre".
Why the -s? If I use the previously mentioned examples we will get they rest - de hviler, they sleep - de sover. My feeling is that the difference is: failing was something that just happened to them and not something they chose, like with the other two verbs. I don't really know, though.
It's a reflexive/reciprocal verb. It looks the same as a passive verb, but it's not. If it helps, imagine there is a seg after the verb. I actually like to look at these as though the initial -s from the seg has been absorbed into the verb, replacing the final -r, and the rest of the seg has been discarded, almost like a contraction. (I don't know that that's what's actually happening, but it's helping me to get my mind around it.) So, when you see this type of verb, you can think of it as a reflexive or reciprocal verb, with a seg following it.
English doesn't have a ton of these verbs, so there's no easy blanket translation: it can translate to 'oneself', 'each other', or nothing at all, depending on the verb. But if you've studied a language like German or Russian, which do, it will make more sense. The best English example I can think of at the moment is 'to enjoy oneself', which translates exactly to the word trives we are learning in this lesson.
Does this mean "Why are they letting each other down/Why are they letting themselves down?"
And, let's say someone has bad grades, how do you say, He is failing the class? Without meaning that he's letting the class down or implying he's the teacher and giving failing grades to all the students. Or does the difference depend on context?
I believe it just means "Why are they failing" or "Why aren't they suceeding?", and we'd need more context to determine what it is they're not succeeding at. The "each other" or "themselves" part doesn't really translate to English; it's simply a part of the Norwegian verb form. In the beginning at least, I think it's best just to learn that mislykkes means "to fail (at something)", remember that is has an -s on the end, and otherwise try to forget that it's special at all.
It is possible that the implied "seg" does represent a long-forgotten reflexive in the dative case. But I don't know the language well enough to be able to say that for certain.