The Halachic term "Achila" ("eating") is generally defined as the consumption of a Ke’zayit within the period of time known as "Kedeh Achilat Paress." There is some discussion as to the duration of time to which this term refers, but we will assume for the purposes of our discussion that "Kedeh Achilat Paress" refers to a period of 7.5 minutes, in accordance with the view of Hacham Ovadia Yosef.
This definition of "Achila" gives rise to the question of whether one is required to recite Birkat Ha’mazon if he ate a "Ke’zayit" of bread over a period of time longer than 7.5 minutes. Does the obligation of Birkat Ha’mazon apply in such a case, or does it apply only when one eats a "Ke’zayit" of bread within the period of "Kedeh Achilat Paress"?
The Peri Megadim (Rav Yosef Ben Meir Teomim, 1727-1792) maintained that as long as the person feels satiated from the bead he consumed, he is bound by the Torah obligation of Birkat Ha’mazon, even though he ate over the course of a period longer than "Kedeh Achilat Paress." The Torah introduces this Misva by commanding, "You shall eat and be satiated, and you shall bless Hashem your G-d," and thus if a person ate to the point of satiation, according to the Peri Megadim, the Torah obligation of Birkat Ha’mazon takes effect.
Hacham Ovadia, however, disagreed. He notes that the Torah requires one to recite Birkat Ha’mazon if two conditions are met – "Ve’achalta," and "Ve’sabata." This means that a person must be satiated ("Ve’sabata"), but also that he must have "eaten" in the Halachic sense, that is to say, he ate a Ke’zayit within a period of "Kedeh Achilat Paress." If either of these two conditions are not met, then the obligation of Birkat Ha’mazon does not take effect. Therefore, Hacham Ovadia argued, just as a person who ate but did not experience satiation is not required to recite Birkat Ha’mazon, because only one of the two conditions were met, similarly, one who feels satiated but did not "eat" in the Halachic sense is not required to recite Birkat Ha’mazon. According to Hacham Ovadia, then, one is obligated to recite Birkat Ha’mazon only if he ate a Ke’zayit of bread within the time-frame of 7.5 minutes.
Intuitively, in light of this difference of opinion, we might assume that an individual in this situation should recite Birkat Ha’mazon, because a Torah obligation is at stake. Since the Peri Megadim maintains that the person in this case is bound by the Torah requirement of Birkat Ha’mazon, we should, seemingly, apply the principle of "Safek De’Orayta Le’humra" – that we must be stringent in situations of doubt involving Torah law – such that the person should recite Birkat Ha’mazon. Just as one who does not remember whether or not he recited Birkat Ha’mazon must do so, since a Torah obligation is at stake, we might assume that in this case, too, given the difference of opinion among the Poskim as to whether Birkat Ha’mazon is required, the person should recite Birkat Ha’mazon.
In truth, however, this is not the case. When one is certain that he was obligated to recite Birkat Ha’mazon, but he cannot remember whether he fulfilled his obligation, he must act stringently because there is no question that there was an obligation of Birkat Ha’mazon. Once it is established that the obligation took effect, one must recite Birkat Ha’mazon even if some uncertainty arises thereafter. In the case under discussion, however, there is a question whether the Birkat Ha’mazon obligation ever took effect in the first place. When faced with such a doubt, one is not required to recite Birkat Ha’mazon, unlike in the case of one who was certainly obligated but was then uncertain whether he fulfilled his obligation.
In light of this dispute among the Poskim, one should endeavor not to place himself in this situation, and should ensure that if he eats a Ke’zayit of bread he does so within a period of 7.5 minutes.
Summary: One who ate a Ke’zayit of bread over the course of a period longer than 7.5 minutes does not recite Birkat Ha’mazon. In order to satisfy all opinions, it is preferable for one who wishes to eat a Ke’zayit of bread to ensure to do so within a 7.5-minute duration.