You are correct. I remember reading in the laws in the back of the Artscroll siddur that you could say it 100 times and be good, but I went back and checked. I found:
75. "On Shemini Atzeres he may repeat the passage mechayeh meisim...one hundred and one times [if he said this only ninety times it is sufficient post facto.]"
And indeed, looking in the Mishnah Berurah 114:37, I found:
"And even though in the next seif the mechaber wrote that 90 times is enough, and in 30 days there are more than 90 [Shemoneh Esreis] because of the Mussaf prayers, many Acharonim have already answered that "30 days" means "like the amount of regular prayers in 30 days", that is 3 times a day. If so, according to their words, we don't need a complete 30 days, but rather once one has completed 90 Shemoneh Esreis one's tongue is immediately accustomed to saying the Shemoneh Esrei as according to Halacha.
And for the matter of "v'tein tal umattar livracha", for in 30 days there are less than 90 Shemoneh esreis (because on Shabbos and Yom Tov [included in the 30 day count] the Shemoneh Esreis only have 7 blessings), a stringency would sprout from this ruling: that one would need to repeat the Shemoneh Esrei [if one isn't sure whether one said "v'tein tal umattar livracha" or not] out of doubt even after 30 days.
And from the words of the Gra and other Acharonim, it is implied that the main principle is dependent only on the passage of 30 days, whether for stringency or for leniency. And as for the practical halacha, we should be lenient on both sides [i.e. either 90 shemoneh esreis or 30 days, whichever comes first], because of the principle that we are lenient with regard to doubts about Berachot.
The Taz writes that if by accident or intent one didn't daven for one or two days from within the 30 days, nevertheless the chazakah isn't damaged and you wouldn't need to wait extra days to make up for the days that you didn't daven."
114:41--"And in the responsa of the Chasam Sopher...he rules that initially, one should say it 101 times; however, bedieved, we can't rule with regard to someone who only said it 90 times that they should go back and pray again, opposite to the Shulchan Aruch's ruling [that you only need to say it 90 times]."
Sorry I quoted the whole thing; I just thought that it was so interesting.
We can learn out a mussar ruling from the Taz: even if you didn't pray for one day--that is, you fell--you haven't lost all your progress, and the chazakah hasn't been destroyed.
Thank you for pointing me to the source in Shulchan Aruch!