His and Not Hers
The Yismach Yisroel explains why Hashem answered Yitzchak's prayer and not Rivkah's, though she too was truly righteous.
Rashi teaches that Hashem accepted Yitzchak's tefillah for children and not Rivkah's, because the prayer of a tzaddik who is the son of a tzaddik is not like that of a tzaddik whose father was wicked. The Yismach Yisroel of Alexander explains the difference. Rivkah was truly righteous, and she davened on the strength of her own merit. Yitzchak had great merit of his own, yet he leaned only on the merit of his father Avraham. The tefillos of the Avos opened paths for their children. Had Hashem answered Rivkah's prayer, the path it opened would have been prayer in one's own merit, and those of us who have none could not follow it. So Hashem answered Yitzchak's humble prayer, and the path stays open for every Jew to pray in the merit of the Avos.
Source: Yismach Yisroel, Bereishis, Toldos (on Bereishis 25:21 and Rashi there; Yevamos 64a)
On a day when you feel you have no merit of your own to stand on, do not stop davening. Before a personal request, in Shemoneh Esrei or in your own words, pause at the first brachah, where we mention the God of Avraham, Yitzchak and Yaakov, and ask Hashem to answer you in their merit. Then make your request simply. The path Yitzchak opened is there for anyone who leans on it, and it does not ask you to be worthy first.