This is a very good question.

(a) In fact if one looks at the SMAG (the Sefer Mitzvos Gadol, written by Rabbi Moshe of Kutzi, who was one of the great Rishonim of Ashkenaz and he lived around the time of the authors of Tosfos) one sees that it is indeed mentioned in his text of the Gemara. (This appears in SMAG - positive commandments #27 page 114a D'H' "Birchos Hoda'ah v'Bakasha". There he cites the passage in the Gemara 60b and HaNotein LaYa'eif Ko'ach is one of the Berachos mentioned.)

The Bach, in his commentary to the Tur Orach Chaim chapter 46 D'H' "Od Berachah Achas" writes that this Berachah was not instituted after the time of the Gemara, but rather that the ancient authorities possessed this text in their version of the Shas. Bach writes "Who could be greater than the SMAG to give us testimony on this, by including in the 18 morning Berachos the blessing HaNotein LaYa'eif Ko'ach"!

The Tur writes that HaNotein LaYa'eif Ko'ach is cited in Ashkenazi Sidurim. This suggests that the Tur did not have it in his version of the Gemara. The Rema Orach Chaim 46:7 writes that the widespread custom amongst Ashkenazim is to say this Berachah.

(b) However in the text of our Gemara, and evidently in the version of many Rishonim (especially the Sefaradi Rishonim) this Berachah does not appear. I would like to suggest a reason why not. This is based on Tosfos Berachos 46a DH "Kol" who discusses the Berachah HaMa'avir Sheinah that we say after Oter Yisrael b'Tifarah and HaNotein LaYa'eif. The question is what is the connection between the start of this Berachah - "who removes sleep from our eyes" - and its conclusion "Who does good Chasadim for His people Yisrael"? Tosfos answers that the Chesed that Hash-m does for us is to remove sleep from our eyes and give us renewed strength . Even though the Neshamah was tired the night before, Hash-m helps us by returning it to us the next morning intact and calm.

According to this, the purpose of the Berachah HaGomel Chasadim Tovim is to thank Hash-m for restoring our strength to our tired soul. It follows that the Berachah HaNotein LaYa'eif Ko'ach is no longer necessary because we thank Hash-m for giving us Ko'ach with a different Berachah.

However the SMAG and the Bach and the Ashkenazi Sidurim maintain that it is not sufficient to thank Hash-m for giving us back our strength with a mere hint, but instead we must devote a separate Berachah to this praise of Hash-m.

This is based on the Beis Yosef in his commentary to the Tur which I cited above. The Beis Yosef writes that he does not know how anyone ever had the right to introduce this Berachah which is not mentioned in the Gemara. This is a different perspective from ours. Since we are accustomed to saying HaNotein LaYaeif every morning we are surprised that we do not see it in the Gemara. Conversely, the Beis Yosef is surprised that it ever became widespread practice to say it since it does not appear in the text of the Gemara possessed by the Rambam, Rokeach and Agur.

(c) Here is a different, and rather simpler, answer to your question. I can suggest a reason why it is not mentioned in the majority of texts of the Gemara. This is because it is a different kind of Berachah than the others. The Gemara states that the other Berachos are said when one does a specific action. For instance there is a special Berachah one says when putting on one's shoes etc. In contrast, HaNotein LaYaeif is a general praise to Hash-m for giving us back our strength. It does not relate to any specific stage in one's morning preparations, and therefore is not consistent with the other Berachos mentioned in the Gemara.

KOL TUV

D. Bloom