The opinion of the Vilna Gaon cited in Mishnah Berurah (475, s.k. 45 and 639, s.k.24) that there is a mitzvah to eat matzah all seven days of Pesach is well known. According to the Gaon there is room to question if one only fulfills the mitzvah with matzos that are made lishmah, or if one can even use matzos that weren’t made lishmah. If we take on that one needs to use matzos that are made lishmah, then the question of machine matzos comes up again, and if machine matzos are not considered lishmah, then although one doesn’t violate the issur of eating chometz when eating them, he won’t fulfil the mitzvah of eating matzah.
In Ma’aseh Rav (ois 186) they relate that the Gaon was particular to eat shmurah matzah from the time of harvesting (משעת קצירה ) the entire Pesach. The Chayei Adam (Klal 128, sif 30) explains that the reason for this is due to various concerns of chometz, such as rain falling on the wheat whilst it is still connected to the ground after the wheat is dry, and sometimes the bags of grain get wet. From the Chayei Adam it seems that the only concern is that it became chometz, however, there is no concern of lishmah and matzah throughout the rest of Pesach (excluding the first night) doesn’t need to be lishmah. According to this approach, machine matzos would be okay.
However, the Demasek Eliezer (siman 453 s.k. 14), R’ Shmuel Salant, and R’ Isser Zalman Meltzer (Eved HaMelech, Shemos 12:17) learn in the opinion of the Gaon that the entire Pesach there is a mitzvas aseh to eat matzah, therefore, when the Torah says “guard the matzos” (Shemos 12:17) from which we learn the din of lishmah as is clear in the Mishnah Berurah (460:3), it would apply the entire Pesach, not just on Seder night. The reason we don’t make a berachah on eating matzah all seven days, is like the Ba’al HaMaor (end of Pesachim 26b, MiDafay HaRif) says, that one can survive seven days without bread, unlike a succah when one can’t survive more than three days without sleep.
In light of this approach, R’ Aharon Kotler zt”l, R’ Moshe Feinstein and R’ Elyashiv all held there is room to be stringent to eat hand matzos the entire Pesach, as they held that according to the Gaon there is a din lishmah the entire Pesach, and there is a better fulfilment of lishmah when using hand matzos.
However, for those who hold that machine matzos are considered lishmah and can be used for the kezaysim on Seder night, certainly even according to the Gaon they may be used the entire Pesach.