The Gemara on Amud Aleph explains why Dovid Hamelech could not offer a reparation to the descendants of Shaul by making a proper but belated eulogy. “It is not the custom to make a eulogy after twelve months.”

Why is it not the custom to do this? Rashi references a Gemara in Moed Kattan (21b) which is not referring only to eulogy, but in general we do not say Hamakom Yenachem after twelve months, because the person is already past the active grief and so it can be hurtful to remind him of the death.

The Rambam (Laws of Mourning 13:10) seems to understand Dovid Hamelech’s rationale for not making a eulogy differently:

אֵין בּוֹכִין עַל הַמֵּת יֶתֶר מִשְּׁלֹשָׁה יָמִים. וְאֵין מַסְפִּידִין יֶתֶר מִשִּׁבְעָה. בַּמֶּה דְּבָרִים אֲמוּרִים בִּשְׁאָר הָעָם. אֲבָל תַּלְמִידֵי חֲכָמִים הַכּל לְפִי חָכְמָתָן. וְאֵין בּוֹכִיִן עֲלֵיהֶם יוֹתֵר מִשְּׁלֹשִׁים יוֹם. שֶׁאֵין לָנוּ גָּדוֹל מִמּשֶׁה רַבֵּנוּ וּכְתִיב (דברים לד ח) "וַיִּתְּמוּ יְמֵי בְכִי אֵבֶל משֶׁה". וְכֵן אֵין מַסְפִּידִין יֶתֶר עַל שְׁנֵים עָשָׂר חֹדֶשׁ. אֵין לָנוּ בְּחָכְמָה גָּדוֹל מֵרַבֵּנוּ הַקָּדוֹשׁ וּשְׁנֵים עָשָׂר חֹדֶשׁ בִּלְבַד נִסְפַּד. וְכֵן חָכָם שֶׁבָּאָה שְׁמוּעָתוֹ לְאַחַר שְׁנֵים עָשָׂר חֹדֶשׁ אֵין סוֹפְדִין אוֹתוֹ:

One should not cry over the deceased for more than three days and one should not eulogize him for more than seven.

When does the above apply? To people at large. With regard to Torah scholars, by contrast, everything depends on their wisdom. In any case, we do not cry over them for more than 30 days, for we have no one greater than Moses our teacher and concerning him, Deutronomy 34:8 states: "The children of Israel cried over Moses... for 30 days and the days of crying in mourning for Moses concluded."

We do not eulogize for more than twelve months, for we have no one of greater wisdom than our holy teacher Rabbeinu Hakodesh, and he was eulogized for only twelve months. Similarly, if a report of a wise man's death reaches us after twelve months, we do not eulogize him.

We see that according to the Rambam, the twelve month limit has to do with showing honor to Rabbi Yehuda Hanasi. How can we dare eulogize for a sage, no matter how great, longer than we did for Rabbi Yehuda Hanasi?

Rambam did not make this up. It is based on a Gemara (Kesuvos 103b) where Rabbi Yehudah Hanasi makes the following request for after his passing:

Rabbi Yehuda Hanasi further instructed: Reconvene the study sessions at the yeshiva after thirty days of mourning. This is because I am not better than Moses, our teacher, as it is written: “And the children of Israel wept for Moses in the plains of Moab thirty days” (Deuteronomy 34:8), which means that for thirty days they wept over him by day and night. From this point forward they eulogized him by day and they studied by night, or they eulogized him by night and studied by day, until they eulogized him for twelve months of the year

Now the plot thickens. Why would Rashi eschew an obvious consideration of the Gemara and offer a different explanation? The obvious answer is that in Shaul’s time Rabbi Yehuda Hanasi was not yet alive, so Rashi (and, we may assume, even the Rambam) needed to explain Dovid Hamelech’s refusal to eulogize Shaul after twelve months. We must also say that according to the Rambam in Laws of Mourning, though he might agree that in general it is unseemly to eulogize more than 12 months, even more specifically post Rabbi Yehuda Hanasi, it would be disrespectful too. 

One other matter remains for us to examine. There is an interesting textual variation when the Rambam discusses 30 days versus twelve months. He states:

וְאֵין בּוֹכִיִן עֲלֵיהֶם יוֹתֵר מִשְּׁלֹשִׁים יוֹם. שֶׁאֵין לָנוּ גָּדוֹל מִמּשֶׁה רַבֵּנוּ

we do not cry over them for more than 30 days, for we have no one greater than Moses our teacher

וְכֵן אֵין מַסְפִּידִין יֶתֶר עַל שְׁנֵים עָשָׂר חֹדֶשׁ. אֵין לָנוּ בְּחָכְמָה גָּדוֹל מֵרַבֵּנוּ הַקָּדוֹשׁ וּשְׁנֵים עָשָׂר חֹדֶשׁ בִּלְבַד נִסְפַּד

We do not eulogize for more than twelve months, for we have no one of greater wisdom than our holy teacher Rabbeinu Hakodesh, and he was eulogized for only twelve months

Rambam refers to Moshe as “no one greater than”, and refers to Rabbi Yehuda Hanasi as “No one greater than In wisdom.” We see the extent of care Rambam used in his choice of words. Moshe’s greatness was a matter that wasn’t necessarily about his intellectual acumen or knowledge base. In fact, we find Midrashic accounts of Moshe’s difficulty in comprehension (for example see Rashi Shemos 12:2, where Moshe has difficulty with the calculations of the new moon, and the structure of the Menorah, Rashi Shemos 25:40).  Moshe was simply “greatest”, not “greatest in wisdom”, because he was, so to speak, the greatest human in his prophetic achievement and attachment to God.  On the other hand, Rabbi Yehuda Hanasi, as great as he was in piety (which is noted in the Gemara), his singular greatness over others was his wisdom in Torah.