Gemara

Rebbi and R. Chiya came to a certain city. They inquired and found that a Chacham lived there. They went to visit him, and received a great Berachah.

The Chacham: I learned the greatness of visiting one's Rebbi from R. Yakov. He used to visit his Rebbi every day. When he grew old, his Rebbi said that he need not do so, for it is too hard.

R. Yakov: "Vi'Chi Od la'Netzach...; Ki Yir'eh Chachamim Yamusu" - one who sees dead Chachamim will live (eternally), all the more so one who sees live Chachamim!

Rosh Hashanah 16b (R. Yitzchak): One is obligated to visit his Rebbi on the Regel. The father of the boy whom Elisha revived asked his wife "Why are you going to Elisha? It is not (Rosh) Chodesh or Shabbos!"

Inference: On Rosh Chodesh and Shabbos one must visit his Rebbi.

Sukah 26b: A case occurred, and R. Ilai went to Lud during the Regel to visit his Rebbi, R. Eliezer.

R. Eliezer: I praise lazy people who do not leave their homes on the Regel - "V'Somachta Atah u'Veisecha".

Question: But R. Yitzchak taught that one is obligated to visit his Rebbi on the Regel!

Answer: That is if he is able to return home the same day (if the Rebbi is within the Talmid's Techum, or through an Eruv).

Rishonim

Rif, Rosh and Rambam (Rosh Hashanah 3b and 1:5, Hilchos Talmud Torah 5:7): One is obligated to visit his Rebbi on the Regel.

Kesef Mishneh: The Rambam did not stipulate that this is only if he can return home the same day. He holds that only R. Eliezer requires this, and the Halachah does not follow R. Eliezer.

Rebuttal (Pri Chodosh, brought in Sefer Likutim in Frankel Rambam): The Gemara challenged R. Yitzchak. It did not answer that the Halachah does not follow R. Eliezer! Rather, if one cannot return the same day obviously he is exempt because of "V'Somachta Atah u'Veisecha". The Gemara thought that R. Eliezer holds that even if he can return the same day, it is better not to go, so that he will have more time for Simchas Yom Tov.

Aruch l'Ner (Sukah 10b DH Shluchei Mitzvah): Rav Chisda and Rabah bar Rav Huna visited the Reish Galusa's house. They consented to sleep in a Sukah in which the decorations were four Tefachim below the Sechach. Rav Nachman said that this shows that they retracted from disqualifying such a Sukah. They denied this. They said that they consented because they are Sheluchei Mitzvah, hence they are exempt from Sukah (Sukah 10b). The Mitzvah was visiting their Rebbi. Rav Nachman held that they are exempt because they could not return the same day; they disagreed. The Rambam rules like them, for they are two against Rav Nachman.

Question: The verse discusses only Rosh Chodesh and Shabbos. Why does R. Yitzchak say that one must visit his Rebbi on the Regel?

Answer #1 (R. Chananel Rosh Hashanah 16b DH v'Akshinan): The Gemara asks this. It answers that if the Rebbi is nearby one must visit him every Shabbos and Rosh Chodesh. If he is far, one must visit him every Regel

Note: It seems that the Rambam did not have R. Chananel's text, for the Rambam never obligates visiting one's Rebbi on Shabbos or Rosh Chodesh.

Answer #2 (Ritva Rosh Hashanah 16b DH Omar R. Yitzchak, Sukah 27b DH Ma'aseh and DH she'Ne'emar): R. Yitzchak gives the minimal obligation to visit one's Rebbi. If one lives in the same city as his Rebbi he must visit him every day. If he is nearby (in the same Techum), he must visit every Shabbos and Rosh Chodesh. If the Rebbi is outside the Techum, R. Yitzchak obligates to visit on the Regel, if he can return the same day. This applies to Chol ha'Mo'ed, for one cannot leave the Techum on Yom Tov.

Answer #3 (Turei Even Rosh Hashanah 16b DH Michlal): In the verse "Shabbos" refers to Yom Tov, like it does regarding Sefiras ha'Omer "Mi'Macharas ha'Shabbos". The verse would not mention Rosh Chodesh before Shabbos, since Shabbos is more frequent. "Rosh Chodesh" refers to Rosh Hashanah, like it says "Tik'u ba'Chodesh Shofar". R. Yitzchak did not need to mention Rosh Hashanah, for the verse says Rosh Chodesh. Even if one would understand this simply, Rosh Hashanah is included. He did not say that one is obligated on the 'Mo'adim', for this would include Yom Kipur.

Answer #4 (Noda bi'Yehudah OC 2:94): On days when there is a Korban Musaf there is more Kedushah. One should visit his Rebbi, because then his Rebbi can influence him more. However, Eibo taught that one need not show more honor to one's Rebbi than to Hash-m (Kidushin 33a). The Halachah does not follow him regarding standing up, for we know that anyone who saw the Shechinah would stand. Regarding a big honor such as visiting we follow him. Therefore, we do not obligate visiting more than one must visit the Mikdash, i.e. on Regalim. Nowadays, the Shechinah is still by the Kosel ha'Ma'aravi, but the Chiyuv to go is only when the Mikdash stands and we can bring Korbanos. Therefore there is no Chiyuv to visit one's Rebbi. This is why the Tur and Shulchan Aruch omit this Mitzvah. The Rambam brought it because it will apply when the Mikdash is rebuilt. The Rif and Rosh cite the Gemara, because it is proper to visit one's Rebbi on the Regel, even though it is not obligatory.

Answer #5 (Pnei Yehoshua ibid. DH v'Amar R. Yitzchak Chayav) Question: How can we learn a Chiyuv to visit one's Rebbi on Shabbos and Rosh Chodesh from the Shunamis? Women are exempt from Mitzvos Aseh sheha'Zeman Gerama!

Answer (Pnei Yehoshua): Really, the Chiyuv to visit one's Rebbi applies constantly. However, because of Bitul Melachah it is limited to days when we do not work. Women should not work on Rosh Chodesh (Tur OC 417). It is like Shabbos for them. Men may work, so they are exempt on Rosh Chodesh. Women are exempt from Talmud Torah, so normally the Mitzvah to visit one's Rebbi does not apply. The Shunamis was regularly by Elisha and recognized his Kedushah, so she was obligated.

Note: The Pnei Yehoshua does not explain why men are exempt on Shabbos. Perhaps indeed they are obligated; R. Yitzchak taught that they are obligated on the Regel, i.e. even on Chol ha'Mo'ed, and all the more so on Shabbos!

Answer #6 (Sefas Emes Sukah 27b DH Eino) Question: How can the Gemara challenge R. Yitzchak from R. Eliezer? Perhaps R. Yitzchak holds like R. Ilai!

Answer (Sefas Emes): We ask how he learns about the Regel from Shabbos and Rosh Chodesh R. Eliezer gives a reason to exempt during the Mo'ed, i.e. "V'Somachta Atah u'Veisecha"! The Gemara answers that when he is able to return home the same day, R. Eliezer's reason does not apply The Halachah follows Chachamim, who obligate in any case.

Poskim

Shulchan Aruch (OC 301:4): (On Shabbos) if one is going to a Mitzvah, e.g. to visit his Rebbi or someone greater than himself in Chachmah, he may go through a river...

Magen Avraham (7): The obligation to visit one's Rebbi is only on the Regel. On Shabbos, it is a Mitzvah, but not a Chiyuv. A woman has the same obligation to visit her Rebbi as a man.

Mishnah Berurah (10): It appears that this is only if her husband permits. (Visiting one's Rebbi is like visiting a parent. A woman cannot leave her husband to honor her parents without permission - Sha'ar ha'Tziyon 12.)

Shulchan Aruch (554:12): On Tish'ah b'Av, one who goes to visit his Rebbi or father... may pass through water.

Magen Avraham (12): He is going on Tish'ah b'Av in order to be able to visit his Rebbi on Shabbos (for then it is a Mitzvah). Alternatively, even though there is no obligation to visit one's Rebbi on a Yom Chol, it is a Mitzvah. The Gemara in Chagigah supports this.

Mishnah Berurah (23): There is no Chiyuv on a Yom Chol, but it is a Mitzvah because one might hear Divrei Torah from his Rebbi.

Aruch l'Ner (Sukah 27b DH Michlal): The Shulchan Aruch does not discuss visiting one's Rebbi during the Regel because it holds that it is a Mitzvah every day, like the Magen Avraham.

Note: It is not clear how this explains the omission, for the Magen Avraham connotes that it is obligatory on Yom Tov, but not on a Yom Chol.

Chayei Adam (Zehirus Mitzvah 68:19 and Nishmas Adam 3): It is not clear whether or not one must go to another city to fulfill a Mitzvah. It seems that this is not required for Teki'as Shofar. However, if one can return on the same day he is obligated, like we find regarding visiting one's Rebbi during the Regel. Surely one with a wife is exempt from this if he cannot return the same day, for it is also a Mitzvah mid'Oraisa to be Mesame'ach her. Also, the obligation does not begin before Yom Tov, and on Yom Tov he may not leave the Techum. However, the Rambam obligates even if he cannot return the same day. This suggests that Simchah does not exempt from other Mitzvos.