Why may one not ask a Chacham about a different Maseches?

Ha'Boneh: This is like it says in Avos (5:7) - one of the Midos of a Chacham is that he asks l'Inyan (what is relevant to what was taught) and answers k'Halachah. Asking a different matter distracts the Rebbi's Sechel and perturbs his Da'as. Also, if he is not a great Chacham, he will answer unlike the Halachah, for he wants to answer immediately. (NOTE: The Mishnah there says that [any] Chacham is not Nivhal (frenzied) to answer! - PF) It says "Machshevos Charutz Ach l'Mosar v'Chol Atz Ach l'Machsor" - it should have said Machshevos Charutz l'Mosar v'Chol Atz l'Machsor! Why does it say "Ach" twice? Charutz is zealous; he prepares before expounding b'Rabim. Atz rushes to speak, without thinking beforehand. The former is praised; the latter is disgraced

Rav Elyashiv: Rebbi is a great Chacham, and answered properly! Why did R. Chiya say that Rav should not have asked him? We must say that even a great Chacham, perhaps he will not know to answer a hard question. Rebbi had special help from Shamayim, and answered properly. L'Chatchilah, one should not ask, and certainly b'Rabim.

A Chacham is proper to be appointed over the Tzibur if one can ask from him a Halachah anywhere, even in [a minor tractate, e.g.] Maseches Kalah (141a). This is even if he is not learning it!

Gilyonei ha'Shas: Usually, a great Chacham can answer anywhere. A minority of the time, because he is learning another Maseches deeply, he will not answer properly. The Talmid must be concerned for this, and not ask until the Rebbi finishes his investigation.

Rav Elyashiv: The Gemara implies that he must be able to answer at any time in the entire Torah!

Rav Elyashiv #1: Below discusses decided Halachos that apply in practice. Nowadays, this is Shulchan Aruch and Poskim. Here Rav asked something not explicit [in prior teachings], which requires investigation, comparisons and a settled mind. Even though here we bring a Beraisa, that was only after Rebbi answered. (Chachamim did not know all the Beraisos; they were not organized.)

Rav Elyashiv #2: One may not ask a different matter in public; it is permitted in private. Nowadays, this does not apply. In our sins, a Chacham is not embarrassed even if he does not know something explicit!

Daf Al ha'Daf citing R. Ovadyah Yosef: One may ask a Chacham when he is not engaged in a particular Maseches. When he is focused on one Maseches, it is hard to divert his concentration to another Maseches. However, Rashi (114a) implies that he can answer even when he is engaged in another Maseches! Minchas Yakov (1) discusses this.