1) Tosfos (46a, DH Ela) writes (in his second answer) that according to the conclusion of the Gemara on 46a, the reasoning of Rebbi Eliezer follows what Rebbi Nasan said, that one may not raise a wild dog or erect a rickety ladder in one's house. Tosfos writes that according to this, if one did not slaughter the Mu'ad he would not be liable for damages. Tosfos calls this an "Isura b'Alma"; it is merely a prohibition to leave the Mu'ad there, but if one did one would not be liable for damages.

Therefore, according to Tosfos, the Mishnah on 55b can anyway not follow Rebbi Eliezer, since the Mishnah discusses when one is liable for damages caused, while according to Rebbi Elizezer, one is never liable for damages caused because one did not slaughter the Mu'ad.

2) According to Tosfos there (46a), I think we have to say that the only reason why the Gemara here (55b) mentions Rebbi Eliezer's opinion is because he is mentioned in the Mishnah together with Rebbi Meir and Rebbi Yehudah; the Gemara did not want to cite the Mishnah in an incomplete form. Otherwise, Rebbi Eliezer is not really relevant to the Sugya on 55b since the Sugya discusses what one has to pay if he does not do the correct Shemirah, while Rebbi Eliezer discusses the way one should do Shemirah even though one cannot be obligated to pay if one did not slaughter the ox.

3) I found bs'd that the Chidushei ha'Rashba (46a, DH Ela) writes that according to Rebbi Eliezer one is not allowed to leave the dangerous ox in one's possession because of Midas Chasidus; it is an act of piety to slaughter the dangerous ox. I think that this brings out even more clearly what Tosfos writes that one would not have to pay if one did not slaughter the ox and it damaged, since it is an extra Mitzvah to kill it, but probably not something expected of everyone. This also answers your question on 55b, since Rebbi Eliezer's opinion is not in the framework of what damage one has to pay for.

4) It is true that Rashi on the Mishnah earlier (45b, DH Ela) writes that according to Rebbi Eliezer, if he did not slaughter the ox and it then damaged, he has to pay for the damage. This does not agree with Tosfos on 46a that he does not have to pay. However, the Tosfos Yom Tov (Peah 2:2) writes that the way of Rashi in many places is to explain in the Mishnah according to what the Gemara thought at the beginning of the Sugya, not according to the conclusion. Tosfos (46a) also writes that in the beginning of the Sugya we thought that Rebbi Eliezer holds that he has to pay if he did not slaughter the dangerous ox, but in the conclusion we say he does not have to pay.

5) Does "Ein Lo Shemirah Ela Sakin" apply to Shen and Regel?

I found, bs'd, that the Talmud Yerushalmi (on the Mishnah at the very end of the fourth chapter of Bava Kama) cites the three opinions of Rebbi Meir, Rebbi Yehudah, and Rebbi Eliezer, and says the following:

"Rebbi Lazer said: For all Shemirah that the Torah said, even if he surrounded the object with an iron wall, one only estimates this in the body. Therefore, we look at it and say, 'If it is capable of being guarded, he is exempt for damage caused, but if it cannot be guarded, he is liable for damages.'"

This is a difficult passage to understand, but I am going to explain according to the Pnei Moshe, printed on the side of the Yerushalmi.

He writes that Rebbi Lazer, mentioned by the Yerushalmi, is identical to Rebbi Eliezer in the Mishnah, and in fact he is now explaining Rebbi Eliezer's opinion. He says that the verse in Shemos 21:36 (which refers to where the ox has gored three times), "And his owners will not look after it," means that once the ox has damaged three times it is a Mu'ad and it is impossible to guard it sufficiently and even an iron wall will not help.

The words "one only estimates this in the body" means that one must slaughter the body of the ox.

I think that the words of the Yerushalmi, "for all Shemirah that the Torah said," come to include Shen and Regel, since the Yerushalmi states "all Shemirah." Once the animal has become Mu'ad by damaging with Shen or Regel, one must slaughter the ox.

So we now have a new answer for why the Gemara on 55b does not say that the Mishnah there can follow even Rebbi Eliezer. This is because Rebbi Eliezer maintains that the Torah does not necessarily require less of a Shemirah for Shen v'Regel if it has damaged three times.

6) The Gemara always tries to have the Mishnah follow Rebbi Meir since an anonymous Mishnah follows Rebbi Meir:

I posed this question to a big Talmid Chacham and he clearly thought it is a strong question. He offered the following answer which he stressed is only a possibility: He answered that the reason why the Gemara here says that the Mishnah is in accordance with Rebbi Meir, and does not say that the Mishnah is accordance with Rebbi Eliezer, is because there is a rule (Sanhedrin 86a) that "Stam Mishnah Rebbi Meir" -- if we do not know who the author of a Mishnah is, we can assume it is Rabbi Meir. Therefore, the Gemara always attempts, if possible, to say that the Mishnah follows Rebbi Meir. Since there is no rule that an anonymous Mishnah follows R. Eliezer, the Gemara did not suggest that our Mishnah is in accordance with him.

I searched a Torah database on this and found that, indeed, the phrase "Afilu Teima Rebbi Meir" occurs a lot more in the Gemara than the phrase "Afilu Teima Rebbi Eliezer." Here are the places that I found where "Afilu Teima Rebbi Meir" appears: Eruvin 95b, Pesachim 41a, Rosh Hashanah 10a, Yevamos 75a and 118a, Nedarim 9a and 63a, Gitin 36a, Bava Metzia 80b, Sanhedrin 15a, Erchin 31b.

The only places I found "Afilu Teima Rebbi Eliezer" are: Ta'anis 4a, Bava Metzia 81b, Horayos 5a, Gitin 86b.

7) There is a big difference between Rebbi Eliezer's opinion and the thrust of the Sugya in 55b:

I posed this important question to a different Talmid Chacham and received a different answer!

He answered that the Sugya on 55b, even before the Gemara explicitly made the distinction between Shen v'Regel and Keren, was -- from the very beginning -- not referring to Keren, so this is not relevant to the opinion of Rebbi Eliezer who refers only to Keren. The only reason why the Gemara there mentioned Rebbi Eliezer is that it cited the Mishnah, so it cited the complete Mishnah.

The Mishnah on 55b refers to a flock going out and damaging, but this is clearly not the damage of Keren. It is damage caused, for instance, when the sheep eat fruit and vegetables or when they enter private land and damage property. Rebbi Eliezer is not discussing this sort of damage. He refers to damage when the animal goes wild and could cause a danger to life. The Sugya on 55b was never discussing danger to life.

According to this, I must retract from the proof that I tried to bring above from the Yerushalmi that Rebbi Eliezer also refers to Shen v'Regel. In fact, one can say that the words of Yerushalmi, "all Shemirah," refers to all Shemirah against Keren. This is backed up by the fact that the verse in Shemos 21:36 (which the Pnei Moshe cites) refers to a goring ox.

I want to try now and bring a proof from the Gemara that Rebbi Eliezer refers only to scenarios where human life may be in danger. This is because Abaye said (46a) that Rebbi Eliezer learns his Din from the Shitah of Rebbi Nasan that one may not raise a wild dog or erect a rickety ladder in one's house. Now the Gemara above (15b) relates that a dog ate sheep or a cat ate chickens. This is unusual and we put the owner in Cherem as long as he does not deal with the problem because of the Din of Rebbi Nasan.

The Shitah Mekubetzes (end of 15b, DH mid'Rebbi Nasan) asks what is the comparison between the dog who ate sheep and the Din of Rebbi Nasan? Rebbi Nasan is referring to danger to human life which does not apply when a dog eats sheep! The Yam Shel Shlomo (Bava Kama 1:45) answers that if a dog eats sheep, this is something very unusual. If a dog is liable to do this he is just as dangerous as a wolf or a lion, so he is a danger to human life and one must kill it. Since Rebbi Eliezer learned his Din from Rebbi Nasan, we see that he must be referring to a potential danger to human life and it is only then that he says that one must slaughter the ox.

Well, we have finally come to the end of this interesting topic, bs'd. I have given a few different answers but I think that, to summarize, we can say that the common factor of most of the answers is that the Shitah of Rebbi Eliezer is quite different from the other Shitos and this is why the Gemara did not mention it (apart from the incidental mention as part of the Mishnah on 55b). According to Tosfos, it is different because Rebbi Eliezer does not obligate to pay. According to the Rashba, it is different because it is Midas Chasidus, and now we have also seen that Rebbi Eliezer requires the animal to be killed only if it might endanger human life, so it is very different to what Rebbi Yehudah and Rebbi Meir discuss.

Kol Tuv,

Dovid Bloom