Indeed, in the responsa of the Beit Halevi (part 3, siman 1), it is raised that the earlier authorities disagree with his words and language. From his words, it seems that he is of the opinion that if someone forgot and drank one of the cups without the required reason, there is no need to go back and drink with the reason, as the two reasons mentioned are not relevant in this case. The first reason is because we don't need to exert effort to fulfill the matter, which only applies at the beginning when coming to drink, where we tell him to reason it out for the sake of being good, but we don't obligate him to drink again for this reason. Additionally, the reasoning of the Ran that we should not be more lenient in this matter than in that matter and uproot the enactment, this also only applies to the establishment of the law, as it is impossible to establish the law to be lenient with either one of them or with both. However, if an individual forgets to reason due to a specific circumstance, this reasoning does not apply at all, and we resort to the general principle of being lenient in cases of doubt concerning rabbinical laws. It is clear that the Rashi and the Ran are of the opinion that if one forgets, there is no need to go back and drink.