1. The Sifri (printed in the Malbim Chumash) on Devarim 17:15 states that the double wording of "Som Tasim" (the Mitzvah to appoint a king) teaches that if the king dies one must appoint another king in his place. This is similar to the examples that the Gemara gives of double wording.

It seems that the reason why the Gemara here does not cite this Derashah of the Sifri is that the Gemara here mentions only Halachos which are applicable nowadays.

2. See the Torah Temimah on Devarim 14:22 who cites the Yerushalmi Shevi'is 2:5 which states "'Aser Te'aser' -- you shall surely tithe -- this teaches that you shall take tithes once a year but you shall not take tithes twice a year." This appears to be an opposite sort of Derashah than those given in our Gemara. In other words, the double wording limits the law and teaches that one may do the activity only once.

It appears from here that a double Lashon teaches that one may (or must) do the act again and again only when it is logical to do the activity repeatedly. If, however, it is not logical to require that one do the act many times (as it is not reasonable to say that one should separate one-tenth of his produce continuosly), then it follows that such a Derashah is not made from the double Lashon.

In addition, there are different things that are derived elsewhere from the double Lashon of "Aser Te'aser." See Ta'anis 9a, where the Gemara learns "Aser," tithe, "she'Tis'aser," so that you should become rich. See also Rosh Hashanah 8a, where the Gemara derives from the double Lashon that not only must one tithe one's grain but one also must tithe one's animals. This is another reason why the Gemara here does not learn from the double Lashon that one may separate tithes many times.

3. Here is another answer to the question from Devarim 17:15:

The main Halachah that we learn from "Som Tasim" is that the king cannot forego his honor, as the Gemara in Kesuvos (17a) states that "Melech she'Machal Al Kevodo, Ein Kevodo Machul" -- the people are commanded to honor the king even if the king does wants to forego his honor.

However, this Mitzvah differs from the other Mitzvos mentioned in Bava Metzia 31a. For example, if one returns a lost object and then the owners lose it again in the main street, when one performs the Mitzvah of returning the object again, it is a new Mitzvah. In contrast, when a king foregoes his honor and the people have a Mitzvah to restore that honor, it is not correct to say that they are making him the king anew every time. Rather, he is the same king all along, but the people have a Mitzvah to maintain that honor continually.

Dovid Bloom