Gemara

(R. Aba bar Zavda): If one gives all his Matanos Kehunah to one Kohen, this brings hunger to the world.

Yoma 26a (R. Chanina): No Kohen ever brought Ketores twice, because it richens.

Question (Rav Papa): Presumably, this is because it says "Yasimu Ketorah b'Apecha...; Barech Hash-m Cheilo";

If so, the same should apply to Olah! The first verse ends "v'Chalil Al Mizbechecha"!

Answer (Abaye): Olah is common. Ketores is not common.

Pirkei d'R. Eliezer (28/29): One who brings his son for Bris Milah is like a Kohen Gadol offering his Minchah and Nesech (wine-offering) on the Mizbe'ach.

Rishonim

Rashi (26a DH Ha): Presumably, what is uncommon richens.

Rebuttal (Tosfos Yeshanim 26a DH Olah): This is not a reason not to richen! Rather, any Kohen who wants can bring a voluntary Olah.

Tosfos (Menachos 50a DH d'Lo): Also Olah richens.

Tzava'as (command of) R. Yehudah ha'Chasid (35/42, cited in Pischei Teshuvah YD 265:15): One should not be Sandek for two sons of a man, unless [the first] one died.

Maharil (Milah 1): When Mahari Segel was Sandek, he would immerse in order to enter the baby to the Bris in Taharah. He said that this Mitzvah is greater than being the Mohel, for his legs are like the Mizbe'ach, as if he offers Ketores to Shamayim. R. Peretz said that we do not give two children to one Sandek. Rather, one chooses another Sandek for each son. No Kohen ever offered Ketores twice, since it richens. Each time, they chose another Kohen. The same applies here.

Poskim

Rema (YD 265:1): The custom is to strive to be Sandek, who holds the baby at the time of Bris Milah. The Sandek is like one who offers Ketores. Therefore, the custom is not to give two children to one Sandek, like it says "Chadashim (new Kohanim come to the lottery) for Ketores!"

Shach (22): I.e. one chooses another Sandek for each son. This is from Maharil.

Birkei Yosef (19): Beis David (122) rejected the source from Maharil. Perhaps the custom in the Rema's area was not to be Sandek more than once in one's life, just like Ketores. This is wrong. The Darchei Moshe says that he learns from Maharil! He did not cite a custom in his place. The Shach is correct. Also Beis Hillel (3 DH Kasav) says so.

Gra (45): This is because Bris Milah is like bringing a Korban, like it says in the Zohar and Pirkei d'R. Eliezer.

Gra (46): There is no reason for this at all. Why do we say that one man should not give two sons to one Sandek? We should say that one may not be Sandek twice [in his lifetime], even for sons of others! We never saw a Sandek become rich [due to the Mitzvah]. Rather, the custom is based on the Tzava'ah of R. Yehudah ha'Chasid.

Noda bi'Yehudah (1 YD 86): Reuven had a son, and the only Sandek he would be pleased with was already Sandek for a previous son. I am reluctant to rule about something without a source in the Gemara. R. Peretz brought a mere Asmachta for the custom. Even if his legs are like the Mizbe'ach, presumably this is the outer Mizbe'ach [and not the inner Mizbe'ach of Ketores], for Dam Bris is like Dam Korbanos! We do not require new Kohanim for Korbanos other than Ketores. It seems that R. Peretz learns from Yalkut Shimoni (Lech Lecha). It says that when Avraham circumcised his household, a mound of foreskins putrefied in the sun. The smell went up to Shamayim like Ketores and like an Olah. Even so, I do not learn from there that it richens, and to require new Sandekim, like Ketores. The Gemara said that we don't require new Kohanim also for Olah, which is frequent, unlike Ketores. Rashi says that presumably, what is infrequent richens. Ketores was only twice a day in the world. It is unlike Bris Milah, which is many times every day in the world. Presumably, such a common matter does not richen. However, Ketores was only for Kohanim, whereas any Yisrael can be Sandek, so perhaps this is not considered common [for a person to be Sandek]. Perhaps this answers why R. Peretz did not insist on a different Mohel for each child. Not all are expert to circumcise, so Bris Milah is considered common for expert Mohelim more than Ketores was for Kohanim. However, Tosfos Yeshanim explains, unlike Rashi, that also Olah richens, even though it is common. In any case, this is mere Drush and hints. It is not Me'akev, and it is not a fixed custom. People are not particular about this in Polin. In many places, the fixed Rav is always the Sandek.

Chasam Sofer (1:158 DH u'Mah she'Chasav): The Rav of the city may be the Sandek every time, for he is like the Kohen Gadol, who offers even Ketores whenever he wants.

Noda bi'Yehudah (ibid.): Ketores was a Mitzvah for all the Kohanim. They are partners in it, so they enacted that no one do it twice. Milah is a Mitzvah on the father. He can choose whomever he wants! I say that R. Peretz compares this to Eruvin 63, in which we say that one should not give all his Matanos Kehunah to one Kohen. This also explains why we are not concerned if different fathers honor the same person to be Sandek.

Rebuttal (Shiyurei Berachah 5): R. Betzalel brings a Tosfos Kesav Yad which cites the Medrash that compares Bris Milah to Ketores, and says that this is why one is not Sandek for two sons of one man. It seems that even though the Mitzvah is common, and it is a mere semblance to Ketores, Chachamim wanted to show that the Mitzvah is dear like Ketores. It is a mere semblance. One may be Sandek for babies of different fathers. The source from Eruvin is unlike the custom that the Sandek gives a gift or money to the father. Also, there one gives food, and here he gives a Mitzvah. R. Peretz did not cite Eruvin, rather, the semblance to Ketores!

Chasam Sofer (ibid.): The comparison to Eruvin 63a is good. However, the custom is not to be Sandek even for one's sons more than once. Surely a Kohen or Levi may keep all his Terumah or Ma'aser! The Segulah to richen does not depend on frequency. Rashi merely said that it is more reasonable to expound that the verse attributes wealth to what is less frequent. If Milah is like Ketores, it richens even if it is frequent! Birkas ha'Zevach challenged Tosfos Yeshanim. If Olah richens, why were they particular that no one offer Ketores twice? Any Kohen who wants to become rich can offer an Olah! I cannot answer this.

Note: One could explain the Gemara to say that Olah is more common, therefore it does not richen as much as Ketores, even if one brings many Olos. Therefore, they were insistent that a new Kohen offer Ketores! However, Tosfos Yeshanim connotes unlike this.

Toras Chayim (Zonenfeld, 15): If the reason is because it richens, the father himself may be Sandek more than once. If it is because it is like giving all one's Terumah to one Kohen, he should not. This is why we do not say about being Sandek that it is better to do the Mitzvah oneself than through a Shali'ach. The Ritva says that we do not require new Kohanim for Olah, for it is impossible. A father can find a new Sandek for each son, but one cannot [always] find one who never was Sandek.

Mishpat Uziel (3 OC 41): There is no Safek that one may be Sandek for all his sons.

Birkei Yosef (19): Beis David (122) said that in Saloniki, the custom is not to be Sandek twice within 12 months, but after that he may be Sandek for any child. In other places they are not concerned for this at all. This is like Olah. Even though it richens, one may offer it many times.

Sha'arei Teshuvah (551:1/3): Perhaps the one who puts the baby on the Sandek's legs may be lenient to shave (during Avelus or in the week of Tish'ah b'Av), for his legs are like the Mizbe'ach. If the Sandek is like the Mizbe'ach, and the Mohel is like the Kohen offering, why can't one be Sandek for two sons of one father? We require Chadashim only for the Kohen who offers! However, I support the custom from Yoma (25b) which suggested making a separate lottery for the incense pan, since it richens, even though the Ketores is merely placed on it.

Chayim b'Yad (73): In some places, one is not Sandek twice in one year. This is like Ketores, just we descend one level. However, people prefer using a Mohel with more experience, and there is a Chazakah to always use the same Mohel. Some say that it is from the first time!

Si'ach Yitzchak (440): The Magen Avraham (551:3) says that the Kvatter (the one who brings the baby) may not wear clean clothes in the week of Tish'ah b'Av. This shows that he is not called Sandek. Therefore, one who was Kvatter may be Sandek for another son. However, Machatzis ha'Shekel brings from Eliyahu Rabah that he is called Sandek. The Gra says that the source is R. Yehudah ha'Chasid's Tzava'ah, for this is dangerous. We must be stringent about a Safek danger (whether Kvatter may be Sandek afterwards).

Aruch ha'Shulchan (34): I think that the source is a hidden matter of R. Yehudah ha'Chasid. Also R. Peretz and the Rema were great in Kabalah. It was proper to give a reason based on revealed Torah which is also true. We should not transgress the Rema's words.

Yechaveh Da'as (3:77): The Mefaresh on Targum Yonason on "Bnei Machir... Yuldu Al Birkei Yosef" (Bereishis 50:23) says that Yosef was Sandek. Yad Sha'ul (265) says that even R. Yehudah ha'Chasid was particular only about a stranger, but one may be Sandek for many sons of a relative. Perhaps the same applies to a Chacham, for everyone is considered his relatives. Many Acharonim say not to be concerned for R. Yehudah ha'Chasid's Tzava'ah, for it was only for his descendants. Even his descendants were not particular to observe it (Shem Aryeh 27)! Surely one may be Sandek for sons of different men, and surely for his sons and relatives. One who observes a Mitzvah will not encounter any evil.