"Are you listening to me?"
Could 'czy' not be used here? I'm sure I've heard it being used in this way before.
Well, you should avoid putting the pronoun at the end of the sentence, if it's possible. And it is possible here, because you could say "Czy mnie słuchasz?", which sounds better (in my opinion).
But frankly, the only two options that I'd recommend are "Słuchasz mnie?" and "Czy ty mnie słuchasz?".
I find it really strange that answers are rejected based on what sounds better in your opinion. This very same discussion has taken place in so many situations, and the bottom line is always the same: even though both options are correct, one option is preferable and hence you simply reject the other option. That's not how languages work and it's not how Duolingo should be teaching languages.
I've just discussed this for the umpteenth time with my significant other (who is Polish and a linguist), and she confirmed again that it's not wrong (nor clumsy) to put the pronoun at the end. While it is better to avoid putting the pronoun at the end, it is not the only option.
Considering that "Czy słuchasz mnie" is 100% grammatically correct, it really should be one of the accepted answers.
Before I address this issue, I need to get something off my chest. We get several commenters a week who try to prove that we are wrong by "having talked to a linguist, professor, native, etc". Those comments make me mad. And this is not because most of those claims are preposterous. It's because the argumentum ad verecundiam just isn't a basis for discussion. And now you're telling us that we make decisions purely based on what sounds better to us. Jellei will never tell you: "Well, I'm a native and this sounds bad. End of story." On the contrary, you will find a reasonable linguistic explanation in every comment. He made no exception here:
Well, you should avoid putting the pronoun at the end of the sentence, if it's possible. And it is possible here, because you could say "Czy mnie słuchasz?"
Now, let me elaborate on that. Polish has accented and unaccented object pronouns. It is obvious that unaccented object pronouns can't be placed in accented positions (e.g. at the very end while other options are available) as that would contradict their purpose. Now, what is mnie? About a hundred years ago, mnie used to be the accented version of mię, but the latter fell out of use, or "dissolved" into mnie, so to speak. So, one can argue that mnie is both accented and unaccented. Hence, there are almost no restrictions regarding the position of mnie within a sentence. So, indeed, "Czy słuchasz mnie?" is 100% grammatically correct.
If a sentence is 100% grammatically correct, does that mean that we have to add it? By no means. And here is a slightly exaggerated example that demonstrates why:
Consider one of the sentences in this course: Mama posprzątała mój pokój. A grammatically correct translation would be: "My mom cleaned my peace." This translation is 100% correct, yet we don't accept it, for obvious reasons. Of course, the matter of czy sluchasz mnie is far less tragic. But we need to draw the line somewhere. Someone has to be the one to make the decision which phrasing is likely enough to be accepted and which isn't. And believe me, that isn't as easy as you think it is.
Now, what's the problem here? The pronoun is put at the end, even though it's avoidable. As a consequence, the logical stress falls on "mnie", so you're basically saying: "Are you listening to ME?" Is that a likely scenario? No, it isn't. Is it possible that a native will use such a sentence, without actually intending to emphasize the pronoun? It is...
But if we accept every possible word order here, we won't be able to teach you the basic rule of pronoun placement. You will be prone to use the same word order as in your native language and you won't learn anything about natural Polish sentence structure. I'm convinced that you should learn the rule first, before you are allowed to break it.
Btw, my go-to Polish language corpus gives me exactly one hit for "Czy słuchasz mnie?" where mnie is put a the end of the sentence. Other options proposed by Jellei yield significantly more results.