The Rama[1] cites and accepts a minhag found in the Maharil[2] not to have one person be the sandek for more than one child in a family.
The Maharil explains the matter. The sandek, who holds the baby during the brit, is like the kohen who offers the daily ketoret (incense) in the Beit HaMikdash. The mishna[3] says that only a kohen who had never offered ketoret in the past was a candidate for a ketoret service. The gemara[4] explains that since the bringing of the ketoret makes one rich, they wanted to “spread the wealth.” The same, say the Maharil and the Rama, is true of a sandek.
However, very important Acharonim question how compelling and binding this minhag is. The Noda B’Yehuda[5] starts off by pointing out that there is no Talmudic source for it; the rationale provided was not the source, but rather helped justify ex post facto a custom that had developed. The Gra[6] also questions the minhag’s Talmudic logic. He notes that if the comparison to ketoret were true, then no one should be the sandek twice, even for babies from different families, whereas the minhag allows this. He also argues that the lack of anecdotal evidence of a correlation between serving as a sandek and wealth raises questions about the validity of the reason given. (Some respond that wealth can come in different forms.) The Gra does not reject the minhag, but says that its real source is the kabbalistic “Will of Rav Yehuda HaChasid.”
The Noda B’Yehuda also accepts the minhag and suggests the following midrash as a source for the comparison to ketoret. The midrash[7] says that when Avraham’s household underwent mila, they piled up the foreskins, which eventually emitted a strong odor. HaShem remarked that the resulting stench was as welcome before Him as ketoret. The Noda B’Yehuda notes[8] that the reason that ketoret leads to wealth is that it is a rare mitzva, as it occurs only twice a day and only in the Beit HaMikdash. On the one hand, that does not apply to mila, which is performed countless times a day throughout the Jewish world. On the other hand, though, since the pool of potential sandeks is so great, it is a rare occurrence for an individual to be a sandek, just as it is for a kohen to bring ketoret. In explaining why the mohel is not at least as comparable to the one who offers the ketoret, the Noda B’Yehuda argues that since the number of mohelim is small, each one performs britot frequently. Therefore, it does not bring them wealth and there is no need to limit a mohel to one brit per family. Despite his explanation, the Noda B’Yehuda reports that not all communities accept the minhag, and he mentions that in some communities, the rabbi serves as the sandek at all britot.
The Chatam Sofer[9] deflects some of the questions and finds a different midrashic source. Regarding the Noda B’Yehuda’s comment about rabbis who are the sandeks at all the local britot, he responds that this is consistent with the Maharil’s primary source. Just as the kohen gadol can bring the ketoret whenever he desires,[10] the community leader can similarly be a sandek as often as he wants, whereas regular people would be limited to once per family.
This brings us to the matter of possible exceptions to the rule. There are minority opinions that: 1) a relative can be the sandek more than once per family;[11] 2) only during a single year should one not be a sandek twice (according to some, even for different families);[12] 3) if the father serves as the sandek, and thus is not giving the honor to anyone, he can do so for as many of his children as he likes.[13] (It is rare nowadays for the baby’s father be the sandek even once.)
In summary, those who do not have a kabbalistic orientation need not take this minhag so seriously, and one need not intervene if another decides to ignore it. However, except when there is a pressing need to reuse a sandek (e.g., in a remote location, where there are very few G-d-fearing people), it makes most sense to follow the accepted minhag that a family honors a different person to be the sandek for each son.