I would like to present a partial answer to this question. I am still waiting for another, official answer.
One of the "pshat"-reasons is that there will be terrible suffering in the generation in which Ben David, Moshiach comes. The ArtScroll version of Sanhedrin (97a, footnote 2) says:
The righteous will die beforehand so that they will not have to endure this suffering. Moreover, such troubles cannot be imposed while the righteous are still living and protecting the people.
So, according to this, "Torah scholars decrease" means that the tzaddikim in our generation(s) will be spared from these troubles, hence they "decrease".
There are several sources that explain that one who clings to a Torah scholar, is considered as if he clings to the Shechina (starting with Kesubos 111b, אגרות ר' יצחק אלחנן, מנורת המאור, אדרת אליהו).
The Lubavitcher Rebbe (Sichos Yud Shvat 5721) explains:
Although the body is a limited physical entity stemming from kelipas nogah, while the soul is “an actual part of G‑d,” the two should ultimately work in harmony. Not only will the body not be negated by the soul, the soul should endow it with life.
Nevertheless, this G‑dly life-energy is hidden, and it is the
responsibility of each person to realize and reveal this potential
through his Divine service. He should come to the awareness that every
one of his limb derives its life-energy from the G‑dly soul. (emphasis mine).
From the explanation of the Rebbe, we can introduce an possible explanation, namely that instead of clinging to the sages, and this way clinging to the Shechina, we need to "work by ourselves" in order to literally "going from strenght to strength" (Tehillim 84:8; see Torah Ohr by the Alter Rebbe, Shemos 1:9 and Torah Ohr Megillat Esther 9:2). Back in the generation of the Gemara, clinging to the sages would mean clinging to the Shechina. But now, we need to cling to G-d by our own effort, seeking G-d through our own efforts, not by simply clinging to the sages.
On the other hand, as I pointed out in the question itself, the sefer מוסרי קלצק explains that we do not have anyone to lean on and to ask halachic questions and how to apply them to our lives. This is, as Rashi writes, the protection offered by the sages in the generation.
Then how do we get protection during the generation in which Moshiach comes? Well, learning Torah ofcourse, but in a broad sense: performing mitzvos, since the very word "mitzvah" is related to the Aramaic word "Tzavsa" which means connection. See for example Hayom Yom; Cheshvan 8:
Mitzva is an idiom of tzavta - "joining," "attachment." Whoever
performs a mitzva becomes joined to the Essence of G‑d - may He be
blessed - Who issues that particular command. This is the meaning of
"The reward of a mitzva is the mitzva (itself)":1 His becoming
attached to the Essence of the En Sof Who ordained the command, is
itself his reward.
Actually, it is a mitzvah to cling to G-d, as the posuk says in Devarim 11:22. The Sefer HaMitzvos says that this can be done, when clinging to a Torah scholar, that is the same as clinging to G-d (see also the Gemara mentioned earlier, including the sources mentioned there.). However, when "Torah scholars decrease", we are meant to find a way to cling directly to Hashem, without the "intermediate step" of clinging to a Torah scholar.