Duo "whilst" is a correct word in English English and can be used instead of "while".
‘While’ is also correct. ‘Whilst’ is more commonly used in British English, but ‘while’ works just as well.
'...during they slept' would be very poor English. You might say '...during the time time that they slept' but even then '...while they slept' sounds better to me.
Why is this sentence not in the genitive case? Isn't 'während' a genitive preposition?
There are plenty of comments saying "whilst" is more usual in English english, so why are Duolingo still refusing to accept it?
I would really like to know what Duolingo has against "whilst" instead of "while". Much more common in English, English.