I recently heard an interesting idea from Rav Schachter, in his Gittin #36 shiur, at starting at about the 16:34 minute mark.
He points to a tiny Tosafot in Gittin 14b that isn’t typically learned in Yeshivot.
Tosafot, d.h. וַחֲכָמִים אוֹמְרִים יַחְלוֹקוּ cite Rav Hai Gaon, in his Shearim of Rabbenu Hai Gaon, of what to do with a תיקו (“the question stands”) across all of Talmud. Namely, that the contesting parties split it. The Ri contested that, and thought this was only when יַחְלוֹקוּ was explicitly specified, but otherwise we would establish the money in its possession of its owner.
That phrasing תיקן only occurs on an איבעיא דלא איפשטא. So, the Chida cites a Shita Mekubetzet that wherever you see Teiku, it is an acronym for Tishbi Yetaretz Kushyot ve’Ibayot. When Mashiach comes, Eliyahu HaNavi will resolve questions and (undecided) queries.
There are two problems with that.
First, there were Amoraim who had revelations of Eliyahu! For instance, Rabbi Evyatar encountered Eliyahu just recently, on Gittin 6b, and asked him about pilegesh be-Giveah. (Eliyahu answered that Hashem simply taught the controversy, about the specific action she took which triggered her husband’s anger. In a follow-up, he said that both had occurred.) So if that is how we resolve unresolved queries, why wait until Moshiach? Why not ask him now?
The Shita Mekubetzet (?) answers that when appearing to Amoraim, he appears as a malach, and a malach isn’t entitled to answer any halachic questions. At the time of Moshiach, he’ll answer as himself, as a human being. (We’d need to also deal with instances of Tanna deVei Eliyahu, which some take as Eliyahu HaNavi teaching things, e.g. in Pesachim 112a, which were taught by Rav Anan — see Ketubot 105.)
But second, as later commentators point out, Teiku only occurs at the end of some Ibayot, unresolved queries, not at the end of (attacking) questions. So, the acrostic isn’t accurate. תיקו is Aramaic for “let it sit stand”, with a root of קום. So why did they allow this false etymology to propagate? Rav Velvele Soloveitchik that the melamdim wanted to be mechazek the emunah in biat haMoshiach, so based on a derasha from elsewhere that said that Eliyahu HaNavi would establish the Sanhedrin the day before Moshiach arrives, they propagated this explanation. But it’s not correct.
This all makes sense and doesn’t need my hearty endorsement. Despite my agreement, I have one reservation about the first objection. Sure, there were Amoraim who had giluy Eliyahu. (Here is a convenient list.) For instance, Rabbi Evyatar was a third-generation Amora of Israel; Rav Anan was a second-generation Amora of Bavel.
But what scholastic generation declared Teiku? And which generations posed the questions to which we hear the answer of Teiku? I understand that these were unresolved questions. But perhaps the dilemmas were posed by earlier generations of Amoraim (such as Avimi or Rami bar Chama) with the expectation that someone in the same, or a later generation would resolve it. Or scholars took different, strong stands about how to resolve the matter, but there wasn’t consensus — just each group having their own proof that the other felt was disproven. And they never resolved it. And then, the Savoraim declared that the question remained.
For instance, in Berachot 8a:
בָּעֵי רַב פָּפָּא: בֵּין פְּסוּקָא לִפְסוּקָא מַהוּ?
Rav Pappa raised a dilemma: What is the ruling with regard to leaving between one verse and the next verse? Is one permitted to leave during a break in the Torah reading while the verse was translated into Aramaic?
תֵּיקוּ.
An answer to this question was not found, so the dilemma stands unresolved.
Did fifth-generation Rav Pappa have revelations of Eliyahu? And who states that the answer is unresolved? (The latest Amora I can think of with an Eliyahu-revelation is fourth-generation Rav Yehuda brother of Rav Sala Chasida, of Bavel, in Yoma 19b.) Is it an Amora who could potentially ask? I don’t think I’ve even seen an answer phrased as Rav Ploni said: Teiku.