The 15-year-old was killed by a Berlin underground train in 2012 and her parents have been trying since to establish if she committed suicide by jumping onto the tracks.
They want access to her Facebook account to examine if she had ever mentioned a death wish in chats with friends or in any posts.
A first Berlin court had ruled in favour of the parents' request, finding that the contents of the girl's Facebook account are part of her legacy.
The panel found that emails and Facebook entries were similar to letters and diaries, which "can be inherited regardless of their content".
But on Wednesday, an appeals court ruled in favour of the US online group, which argued that opening up the account would compromise the privacy of the teenager's contacts.
In a recent high-profile court case, the website clinched victory against a Syrian refugee whose selfie with Chancellor Angela Merkel made him the target of racist trolls.
The refugee had sought to get the online group to search out and delete defamatory posts, but the court ruled that it was unclear whether Facebook was able to conduct such searches without surmounting major technical hurdles.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)