It seems to be a common theme in the prayer service that we ask for our needs basing our requests on the mercy of G-d, and, occasionally, on the merit of our forefathers. Nonetheless, we find some examples where we seem to base our requests on the merit of our actions. For example, in the Ashkenazi Shacharith Tachanun service of the second and fifth days of the week, we have the supplications:
וְחון אם הַמְיַחֲדִים שִׁמְךָ פַּעֲמַיִם בְּכָל יום תָּמִיד בְּאַהֲבָה וְאומְרִים שְׁמַע יִשרָאֵל. ה' אֱלהֵינוּ. ה' אֶחָד:
...and show favor on the nation that unifies Your name twice daily continuously with love saying: "Hear Israel, the L-rd our G-d, the L-rd is one."
as well as:
וּבְכָל זאת שִׁמְךָ לא שָׁכָחְנוּ. נָא אַל תִּשְׁכָּחֵנוּ:
...and with all this we [still] have not forgotten Your name, please don't forget us.
What is the origin of these formulations?