Why does the Torah repeat "Mo'adei Hashem"?
Rashi: Pasuk 2 is referring to arranging an Ibur Shanah (a leap-year), 1 and the current Pasuk, to Kidush ha'Chodesh - the Mitzvah on Beis-Din to sanctify each month. 2
Ramban: Refer to 23:3:1:3*.
R. Bachye: "Eileh" implies permanence - to teach us that the Yamim-Tovim will last forever, as long the world exists in its physical form. 3 4
See also R. Bachye citing Pirkei de'R. Eliezer, who describes in detail 'Ibur Shanah' - which could only be performed by the Sanhedrin in Eretz Yisrael - though the Gemara in Rosh Hashanah 25a rules that if the Gadol ha'Dor is in Chutz la'Aretz, then he should arrange Ibur Shanah.
Refer to Shemos 12:2:1-6 where many details connected with these issues are discussed in detail.
See R. Bachye.
R. Bachye: And it is about them that the Pasuk writes in Tehilim 111:8, "Semuchim la'Ad l'Olam. Asuyim be'Emes v'Yashar."
How will we reconcile "Eileh Mo'adei Hashem" with "Asher Tikr'u Osam" (which we expound as 'Atem' - you)?
Yerushalmi Rosh Hashanah, 1:3: 'Until now they were My festivals; from now on they are your festivals!' 1
See Torah Temimah, note 13.
What are the connotations of the word "b'Mo'adam'?
