For what it’s worth at this late date, I agree with @Gilles' comment under the question that “It’s not over until the fat lady sings” (hereinafter "the F.L. Expression"), and it’s shortened version as mentioned by Benjol: “it [ain’t] over ‘til it’s over,” are both neutral expressions (“ neutre vis-à-vis du caractère bénéfique ou non de la situation”) that are merely stating the obvious that outcomes can change, for better OR for worse, right up until the outcome becomes officially final.
The F.L. Expression is often used by coaches of sports teams (and politicians) to either:
1) CAUTION their team (or campaign workers) not to prematurely celebrate victory just because they are ahead in the game (or in the pre-election polls) because the game (or election) is not yet “over” or finished and there is still time to mess-up and lose the game (or election);
2) ENCOURAGE their team not to prematurely give up/admit defeat just because they are losing because there is still time to come from behind and win.
Cautioning against “counting chickens” or “selling bear fur” prematurely would certainly capture the F. L. Expression’s meaning in #1, where it means “cautioning against premature victory celebrations”, but I’m not convinced that they are neutral enough to accurately capture the F. L. Expression’s meaning #2, where it means “encouragement not to prematurely admit defeat.”
(Of course, if “don’t sell the bear’s fur ‘til it’s dead” also means “don’t mourn yet for the poor bear because there is still time to save him,” then it might also capture meaning #2 of the F. L. Expression. However, my French wife assures me (and right or wrong, I usually listen to her) that the “bear fur” expression is not neutral, i.e., that it is ONLY a caution against acting foolishly and celebrating prematurely and that it is not meant to be interpreted to include the notion of “it’s not too late to save the poor bear.”)
The popularization (although not its origination) of the F. L. Expression has been attributed to Dan Cook, a TV sports editor, and its shorter version to Yogi Berra, a well-known baseball player, coach, and coiner of expressions.
In light of the the above-mentioned indirect connections to the world of sports and its direct connection with theatre/opera, I think that suitable French translations of the neutral notion of the F. L. Expression could/should also connect with either sports/games(competitions) or else the world of theatre, which, in my opinion, Gilles’s « Tout n'est pas encore joué » and Amphiteóth's « Tant que le rideau n'est pas tombé, la pièce n'est pas terminée » both do very nicely.
Additional neutral, sports-related options could include the following translations/paraphrases of something that Rocky Balboa said in "Rocky V ("a fight ain't over till you heard the bell"):
« C'est pas fini tant que la cloche n'a pas sonné ! »
« C'est pas fini tant que le gong n’a pas retenti. »
And finally, in the context of the "sport" of romance, I think that Hélène Ségara captures nicely the neutral notion near the end of her song “Avant la fin”:
Avant la fin, [entre nous deux,] rien n'est fini...