Does the ban have an expiration date and what is the status of the ban today:[1]

Tradition of year 5000 expiration: Many Poskim[2] record a tradition and rule that the ban which was initially made by Rabbeinu Gershom had an expiration date of the Jewish calendar year 5000, and hence was only imposed for a period of about 200 years. [Accordingly, some Poskim[3] are of the position that it would be better if this ban would be abolished.] Other Poskim[4], however, argue on this tradition.

The custom today:[5] Nonetheless, despite the expiration date, the accepted custom was to be stringent and extend the ban even after the expiration date, and therefore this ban remains in place even today, and even in today’s times it is forbidden to marry more than one wife, due to the tradition and custom. [This certainly applies according to all the Poskim[6] who argue on the above expiration date, and negate the above tradition.]

Enforcing the ban today: Some Poskim[7] rule that if one transgresses this ban, then even today we excommunicate him and force him to divorce one of his wives. [He is forced to divorce his second wife, unless his first wife agrees to get divorced.[8]] Other Poskim[9], however, rule that due to the above tradition, the ban can no longer be enforced today. Practically, however, we do not rule like this opinion, and the ban is enforced even today.[10]

100 Rabbis: Due to the above expiration date tradition, some Poskim[11] rule that in today’s times it is no longer necessary to get a Heter from 100 Rabbis to marry a second wife, in those cases of justifiable reason to be explained. Other Poskim[12], however, rule that it is required even today, and so is the practical ruling.

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[1] See Pischeiy Teshuvah 1:19; Encyclopedia Talmudit Vol. 17 Erech Cherem Derabbeinu Gershom sec. 3 p. 384 and onwards

[2] Michaber E.H. 1:10 “the ban was made only until the year 5000”; Maharik Shoresh 101, brought in Beis Yosef 1:10 and Darkei Moshe 1:9 and so he concludes as fact; Shut Beis Yosef Dinei Kesubos 14; Teshuvas Harashba [see 2:230; 4:186]; Teshuvas Rabbeinu Tam Ben Yichyeh in Tomas Yesharim 202; Radbaz 1180; 2:700; Sheilas Yaavetz 2:15; Mishkanos Yaakov E.H. 1, brought in Pischeiy Teshuvah 1:19; Eiyn Yitzchak 1E.H. 4:20; Avnei Nezer 1:8-8; See Mabit 3:6; Encyclopedia Talmudit ibid footnotes 65-66 and 69

[3] Sheilas Yaavetz 2:15

[4] Some Poskim negate the above tradition, and state the ban of Rabbeinu Gershom was applied for all times without any expiration date, and has hence not been relied upon by any of the Poskim to be lenient. [Yam Shel Shlomo Yevamos 6:41 and Shut Maharshal 14 in name of Or Zarua, Mordechai, Semak and that so is evident from the fact that no expiration date was mentioned in the original ban that was issued; Riy Di Miluni brought in Shut Beis Yosef; Maharashdam Y.D. 140; E.H. 120 in name of Yechiel Ashkenazi; Maharshach 2:36, brought in Kneses Hagedola 1:55; Maharam Alshiker 95, brought in Kneses Hagedola 1:56; Chacham Tzevi 124; Chasam Sofer C.M. 203; E.H. 2 that the above Achronim would have retracted their opinion if they would’ve seen the words of the Rashal ibid; Mishkanos Yaakov E.H. 1, brought in Pischeiy Teshuvah ibid; See Encyclopedia Talmudit ibid footnotes 70-5 Otzer Haposkim 1:76]

[5] Rama E.H. 1:10 “In all these provinces, the ban and custom remains and we prohibit polygamy under threat of excommunication”; Darkei Moshe 1:9 “Although we are still accustomed to follow the ban of the Gaon, nevertheless, the decree has already been nullified and from here and onwards that ban is merely due to accustomed stringency, which is forbidden to be permitted”; Rosh Teshuvah 43:7, brought in Beis Yosef 1:11; Shut Haran 48; Shut Beis Yosef ibid; See Maharashdam E.H. 78; Pnei Moshe 2:117; Encyclopedia Talmudit ibid footnote 67-68; All Poskim ibid who argue on the expiration date

[6] See other opinions above

[7] 1^st opinion in Rama E.H. 1:10 and that so is the custom; See Pischeiy Teshuvah 1:20

[8] Beis Shmuel 1:24; Chelkas Mechokeik 1:8

[9] 2^nd opinion in Rama E.H. 1:10; Beis Yosef E.H. 76, brought and negated in Darkei Moshe 1:9

[10] Rama E.H. 1:10; Darkei Moshe 1:9; See also Michaber E.H. 1:11

[11] Darkei Moshe 1:9, brought in Beis Shmuel 1:23; Tosafos Beitza 5a; Hagahos Ashri Beitza 3; This requirement is omitted from the Rama in his Shulchan Aruch; See Encyclopedia ibid footnote 830

[12] Beis Shmuel 1:23 and 119:8 in name of Bach that so is a Kabbalah from previous generations; Chelkas Mechokeik 1:16 and 119:7; See Pischeiy Teshuvah 1:16; See Encyclopedia ibid footnote 831