Related is this question, but I think it's waaaay too narrow in focus.
In fact, I went through the entire Torah, picking out any place where a year contained more than one nonzero digit and sorted them by two digits versus three digits and by whether Shanah is repeated (ha) or not. Here are my results.
Three Digits
Repeats
Asterisks are the ones addressed by Rashi and the aforementioned question
Adam (Bereishis (5:5)
Sheis (Bereishis 5:6-8)
Enosh (Bereishis 5:10-11)
Keinan (Bereishis 5:13-14)
Mehallalel (Bereishis 5:15-17)
Yered (Bereishis 5:18,20)
Chanoch (Bereishis 5:23)
Mesushelach (Bereishis 5:25-27)
Lemech (Bereishis 5:28)
Noach (Bereishis 9:28-29)
Arpachshad (Bereishis 11:13)
Shelach (Bereishis 11:15)
Eiver (Bereishis 11:17)
Peleg (Bereishis 11:19)
Re'u (Bereishis 11:21)
Nachor (Bereishis 11:25)
Terach (Bereishis 11:32)
*Sarah (Bereishis 23:1)
*Avraham (Bereishis 25:7)
*Yishmael (Bereishis 25:17)
Yitzchak (Bereishis 35:28)
Repeats for 2/3 digits
Lamech (Bereishis 5:30-31)
Yaakov (Bereishis 47:28)
Doesn't repeat
Adam (Bereishis 5:3)
Yaakov (Bereishis 47:9)
Yosef (Bereishis 50:22,26)
Levi (Shemos 6:16)
Kehas (Shemos 6:18)
Amram (Shemos 6:20)
Years spent in Mitzraim (why limit it to people? - Shemos 12:40-41)
Aharon (Bamidbar 33:39)
Moshe (Devarim 34:7)
Two digits
Repeats
Avraham (Bereishis 12:4, 16:16)
Yaakov (Bereishis 47:28)
Doesn't repeat
Arpachshad (Bereishis 11:12)
Eiver (Bereishis 11:16)
Re'u (Bereishis 11:20)
Avraham (Bereishis 17:24)
Aharon (Shemos 7:7)
Yovel (Still not limiting it to people - Vayikra 25:8)
Age of Leviim (Bamidbar 8:24)
So... In conclusion, if the number is three digits, it tends to repeat Shanah after all of them, while it's the opposite if it's two digits. There are exceptions to both. Notice how certain people, like Avraham (who Rashi asked about) appear in both categories. Notice also that although Yaakov appears in both categories, everyone who lived after him - and our non-people which also appear after Yaakov's death - appear only in the "doesn't repeat" category, regardless of the number of digits.
Why this is the case is for another question. My question is: why does Rashi make such a big deal about Sarah and Avraham, and the Maskil L'Dovid on Yishmael, when that seems to be perfectly normal in the Torah?