"Was war die Begründung für diese wieder?"
The solution is the following: Someone is notoriously making excuses in a very annoying way to the same/similar question. And the person who is asking the question to the "bad boy" asks in disbelief "What was the reason for this one (question) again. In German: Was war die Begruendung fuer diese (Frage) wieder? (Diese Frage is obviously a popular/re-occurring question, that's why this one (specific one). It is a single question, hence "diese" (sing) = this one in the above case. :-)
because it relates to diese (eine) Frage = this (one) question, which is Singular, and Plural would be: diese Fragen = these questions. It is not easy to explain, nor is it obvious from the given text. I only tried to give a context in which the question may have had been said, see my above text. This is the only scenario the whole thing makes sense to me. Again diese Frage is (sin) and diese Fragen is (pl) and Frage is a word which I think is the one it relates to, even if it does not occur in the text. From the article alone you cannot conclude if it is singular or plural. For my understanding it relates to a single question, and therefore it is diese = this one and the English translation is correct. I the hope not to confuse, more than to clarify.
Let me restate my questions: 1. why singular only is allowed as the translation? 2. can "diese" here mean plural?
You've invented one single scenario and work around it. That's ok. But as you can see from 1. and 2. I never asked about the meaning of this sentence and how it is understood by others. I'm interested in proper grammar. Is there any grammatical indication that "diese" here is strictly singular feminine? If yes, I'd like to know what it is. If not, then there is a bug at Duolingo for that excersise, that's all.
to 1: I don't know, it is wrong! (I have reported it now) to 2: yes it can, see below.
"Was war die Begründung für diese (Frage |fem||sin|) wieder?"
"Was war die Begründung für diese (Fragen |fem||pl|) wieder?"
"Was war die Begründung für diesen (Fehler |m||sin|) wieder?"
"Was war die Begründung für diese (Fehler |m||pl|) wieder?"
"Was war die Begründung für dieses (Fehlverhalten |neu||sin|) wieder?"
"Was war die Begründung für diese (Fehlverhalten |neu||pl|) wieder?"
The above are 3 examples are correct German questionss, me just grasping what it could have meant here. The first is the relevant one, the others only to show that it differs for other genders. I used three examples in genders and |sin/pl| form. You see that for the male and the neuter you can determine from the article diese(n) or dies(e) that it would be singular, when it comes to female diese and diese stand for both |sin||pl|. If you don't have the ending of the dropped substantive (in my first example "Frage") you can't use the ending of the substantive to determine if it is singular of plural. Conclusion, you cannot determine in our case from the given sentence, if it is singular or plural, and that's why DUO should have allowed a second answer at least like: "What was the reason for these (questions) again? For more info: http://en.wikipedia.org/wiki/German_declension#Definite_articles.5B1.5D