בראשית כ:א,ב - ויסע משם אברהם ארצה הנגב וישב בין קדש ובין שור, ויגר בגרר. ויאמר אברהם אל שרה אשתו אחתי הוא וישלח אבימלך מלך גרר ויקח את שרה.
20:1,2,5 record that Avraham and Sara went to live in Gerar, and when they got there, they told people that they were brother and sister. This is similar to what they had said when they went to Egypt, 12:11-15, and just like in Egypt, Pharaoh’s servants took Sara, in Gerar, the king of Gerar, Avimelekh took Sara. Apparently, Sara's youth and beauty had returned to her even though she was old as part of the miracle that she would give birth at ninety (Rav Hisda quoted in Talmud, Baba Metzia, 87a).
Why did Avraham and Sara again try to conceal their marriage if Sara was abducted in Egypt when they used this plan? Why did they not learn from the previous case?
When Avraham and Sara went to Egypt, Avraham said that it was necessary to conceal their marriage to save his life, 12:12. In Gerar, was Avraham again worried for his life? 20:11 records that when Avimelekh questioned Avraham for why he concealed his marriage, he said that he was afraid of being killed. Yet, was this fear a sufficient reason for Avraham and Sara to conceal their marriage a second time? The Radak (on 12:12) justified Avraham and Sara’s actions in Egypt since a person cannot rely on miracles. Yet, the ploy failed in Egypt. Would it not have been preferable for Avraham and Sara to say they were married in Gerar and take their chances that nobody would try to kill Avraham and abduct Sara?
The cynic might argue that Avraham and Sara learned from the case in Egypt to rely on this ploy since everything was good in the end as Avraham was not killed, Sara was returned and they received lots of gifts. This possibility must be rejected since from chapter 14 we learn that Avraham no longer wanted to receive gifts. 14:22,23 record that after Avraham defeated the five kings, he refused to keep any of the booty from the war, so that nobody could claim that they made him wealthy. In this case, Avraham did accept gifts from Avimelekh, 20:14-16, but this was after the fact and necessary to show that there were no sexual relations between Avimelekh and Sara. Also, the success in Egypt was due to a miracle, so with this approach, one would have to argue that now Avraham and Sara were relying on a miracle, that if Sara would be abducted again, then G-d would do a miracle to save her. Yet, if that is true, then they could have said that they were married and relied on a miracle that Avraham would not be killed.
A second possibility why Avraham and Sara concealed their marriage in Gerar is that Avraham and Sara thought that their plan was good and just because it failed once this was no reason to discard it. Maybe they thought that they just had bad luck in Egypt, but otherwise the plan would have succeeded. 20:3 records (see also Ramban on 12:12) that Avraham said that he and Sara always claimed that they were brother and sister, and not husband and wife, whenever they traveled and then it could be that Torah only records the places where there were problems.
Was Avraham really scared of being killed in Gerar? The Avraham of chapter 20 was not at all like the Avraham (Avram) of chapter 12. The Avraham of chapter 20 had fought a war against five kings, chapter 14, made two covenants with G-d, chapters 15 and 17, and had been able to argue with G-d about the fate of Sedom, 18:23-32. It is unlikely that Avraham would have such a great fear of mankind. Furthermore, Avraham had twice been told that he would have a son with Sara within the year, 17:21 and 18:14. Did Avraham think that G-d was promising him a son, but that he would not live to see it? It is true that in 20:11 Avraham mentioned that he was worried about being killed but this fear is mentioned after Avimelekh learned that they were married, and maybe in 20:11, Avraham mentioned this fear to turn "the tables" on Avimelekh that really the situation was Avimelekh’s fault since in his domain nobody was G-d fearing.
Independent of whether Avraham was scared of being killed, maybe Avraham and Sara had another reason to conceal their marriage in Gerar. Avraham and Sara arrived in Gerar not long after the destruction of Sedom, and even though Lot was saved, it was highly likely that Avraham was very upset by the destruction of Sedom. Avraham had prayed fervently for the city, but G-d had ignored his pleas and destroyed the city. This despondency might explain why he concealed his marriage.
The beginning of 20:1 records how Avraham, and apparently Sara, were roaming in the Negev (today the area of the northern Negev) prior to them coming to Gerar. This roaming could have been because of his sadness after the destruction of Sedom, and if so, then it is likely that he also wandered alone for some time. This would have meant separating from Sara now and then. However, people would begin to ask why was he alone without his wife? Therefore, Avraham and Sara said that they were brother and sister, which they were, 20:12, without revealing that they were also married, to stop people from thinking that they were having marital problems, especially as Yitzhak was supposed to be born soon. The idea was to enable Avraham to have time to be by himself. With this idea, Avraham and Sara would have known that there was a risk that somebody would abduct Sara since she was a "single woman" but they thought the risk was very low and worth the benefit of people not bothering them about their marriage.