Being a Sandek for two sons of a father:[1] [Tzavah of Rav Yehuda Hachassid/Achronim]

A person should not be a Sandek for more than one son of an individual, unless the previous son has died r”l. [This is practiced even today.[2] Some are stringent in this even if the child has died.[3] If one is unsure if a person has already been honored to be the Sandek for one of his sons, he is to be stringent.[4]]

Father of child: Some Poskim[5] rule that this restriction applies even to the father of the child that he should not be a Sandek for more than one of his sons. Other Poskim[6], however, rule that there is no issue for a father [and some say even other relatives[7]] to be a Sandek for more than one of his sons.

Is the prohibition on the Sandek himself: Some Poskim[8] rule that this prohibition only applies to the father of the child, that he may not honor the same person to be Sandek twice. However, if a person was offered to be Sandek for a second son, then there is no prohibition for him to take it. Other Poskim[9], however, rule that the worry applies both to the father of the child and to the Sandek himself, and hence he is to refuse being Sandek for more than one child.

Rav of city: Some Poskim[10] permit to make an exception for the Rav of the community, that he may be Sandek for more than one son of the same father. Other Poskim[11], however, are stringent even in such a case.

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[1] Tzavaas Rebbe Yehuda Hachassid 40 [or 35 or 42, depending on print]; Pischeiy Teshuvah Y.D. 265:15; Shemiras Hanefesh 138; Kaf Hachaim 116:183; Sefer Shemiras Haguf Vihanefesh [Lerner] 150:2-8

[2] Other opinions: Some write that in today’s times we no longer suspect for the above matter and hence one may be a Sandek for two children of the same father. [Shemiras Hanefesh 139; Kaf Hachaim ibid; See Noda Beyehuda Kama Y.D. 86; Yechaveh Daas 3:77; Sefer Shemiras Haguf Vihanefesh [Lerner] 150:10]

[3] See Shivim Temarim ibid; Sefer Shemiras Haguf Vihanefesh [Lerner] 150:7

[4] Shivim Temarim ibid; Sefer Shemiras Haguf Vihanefesh [Lerner] 150:8

[5] Chasam Sofer O.C. 158 [that so is the custom, although he questions this on the basis that a Kohen may withhold his Matanos for himself]; Igros Kodesh 12:444 [in answer to Rav Meir Avtzon a”h who wanted to be a Sandek a second time by one of his sons Mila; Shevach Habris 17:6  

[6] Migdal Oz 9:5; Siddur Yaavetz; Shivim Temarim on Tzavah Os 40; Yad Shaul Y.D. 265; Zecher Dovid 1:75; Sefer Shemiras Haguf Vihanefesh [Lerner] 150:5

[7] Yad Shaul Y.D. 265 [i.e. grandfather and other relatives]; However, see Shivim Temarim ibid who negates this and says the allowance is only for the father; See Sefer Shemiras Haguf Vihanefesh [Lerner] 150:6 footnote 9 

[8] Yad Shaul Y.D. 265; Mili Dechassidusa

[9] Shivim Temarim 12

[10] Noda Beyehuda Kama Y.D. 86; Chasam Sofer O.C. 158; Shaareiy Teshuvah O.C. 551:3; Y.D. 265:14; Chasam Sofer; Mili Dechassidusa 40

[11] Shivim Temarim 12