The Gemara in Kiddushin 29a derives from a pasuk in this week’s parshah that women are exempt from performing a bris milah on their sons. The pasuk says: “ka’asher tzivah oso Elokim” (Bereishis 21:4). The Gemara takes from the word “oso” (him) that women are exempt. The Rishonim there are disturbed by the following question: why is it necessary for this pasuk to be written in the Torah when it is a mitzvas assei she’hazman gramma (time-sensitive mitzvah), which women are exempt from performing?
Tosafos answers that since from the eighth day forward the mitzvah is continuous, it is not considered a mitzvas assei she’hazman gramma. Tosafos then points out that this answer is only applicable according to the opinion that holds that after the eighth day a bris milah may be performed at night as well as by day. For according to the opinion that a bris milah can only be performed by day, the mitzvah is not continuous – as it cannot be performed by night.
Some Acharonim ask on Tosafos that according to everyone one may not perform a bris milah on Shabbos or Yom Tov if it is after the eighth day. Thus, according to all opinions, the mitzvah should not be considered continuous.
Rav Akiva Eiger, zt”l, writes that this question does not even begin. He explains that the only thing that renders a mitzvah to be non-continuous is if there is a halacha of the mitzvah that dictates that it cannot be performed at this time. For example, since there is a halacha in bris milah that the bris may not be performed at night, the mitzvah is considered to have a time whereby it is not applicable and thus is considered a mitzvas assei she’hazman gramma. However, the reason that a bris may not be performed on Shabbos and Yom Tov by a Jew is not a halacha of bris milah but rather a halacha that on Shabbos and Yom Tov one may not make a wound. This results that a bris may not be performed.
But as far as the mitzvah of bris milah is concerned, it may be performed on Shabbos and Yom Tov. According to one opinion a non-Jew can perform a bris milah; if he were to perform the bris on Shabbos, it would be valid. We can compare the fact that we cannot perform a bris on Shabbos and Yom Tov to one who does not have a knife. The mitzvah applies except that one does not have the necessary equipment to perform the mitzvah on Shabbos. Thus the fact that it may not be performed on Shabbos or Yom Tov is not a reason for the mitzvah to be considered a mitzvas assei she’hazman gramma.
On a similar note the Shagas Aryeh (Turei Even Chagigah 16b d”h bnei) writes a novel idea on the matter. He begins with a Gemara in Pesachim 84a that says that women are obligated in the mitzvah of burning nosar (the leftovers of a korban). He asks: the Gemara says in Yevamos 72b that nosar must only be burnt during the day, not at night. It should then result that the mitzvah of burning nosar is a mitzvas assei she’hazman gramma. Why then are women obligated in this mitzvah?
The Shagas Aryeh says that the only time a time restriction renders a mitzvah a mitzvas assei she’hazman gramma is when the time restriction takes away from the performance of the mitzvah. For example, if the mitzvah of tefillin would exist at night we would be obligated to wear tefillin for the entire night. Since we are not obligated to wear tefillin at night, the time that we are obligated to perform the mitzvah is lessened. However, a mitzvah such as burning nosar is a one-time action; once it is burned the mitzvah is complete. The fact that we may not burn nosar at night does not lessen the mitzvah; it only gives us less time to perform that mitzvah. The Shagas Aryeh suggests that the only time restriction that creates a mitzvas assei she’hazman gramma is one that makes the mitzvah less – not one that restricts the time that one can do the mitzvah.