Mishna Berura 478:1:2 says that you should not drink anything other than water after the Afikomen in order not to lose the flavor of the Matza. How then can we drink cup 3 and cup 4 of wine after the Afikomen? Does that not take away the flavor of the Matza?
The gemara (P'sachim 119b) mentions the prohibition of eating after the the final matzah (which is known nowadays as the afikoman). There are different opinions among the poskim as to the reason for this. The Rashbam (ad loc., s.v. אין מפטירין אחר המצה אפיקומן) writes that the reason is to prevent attenuating the taste of the matzah, which is eaten as a remembrance to the matzah that was eaten with the korban pesach. The Rif (P'sachim 27a) writes that one who is thirsty may drink only water after the afikoman. The Rambam (Hil. Chameitz uMatzah 8:9,10) rules likewise, and seems to say the the reason for prohibiting both eating and drinking is to preserve the taste of the matzah in one's mouth.
The Rosh (P'sachim 10:34) writes that the afikoman is a remembrance to the korban pesach itself, after which dessert could not be eaten. However, he rules based on the Y'rushalmi (P'sachim 10:6) that the reason for not drinking more wine is to remain sober enough to stay awake and expound on the exodus from Egypt. Therefore, he rules, drinking anything aside from alcoholic beverages is permitted after the afikoman. The Tur (OC 481) quotes the same ruling in the name of Rabbeinu Yonah.
The Ran (Chidushei HaRan, P'sachim 119b) writes that wine does not attenuate the taste of the matzah enough to be a problem. Rather, he writes, the reason for not drinking more is to not disrupt the symbolism of the four cups of wine instituted by the sages. In his commentary on the Rif (ad loc.) he suggests that adding extra cups of wine would give the appearance of starting a new seder, which would at least symbolically controvert the prohibition against partaking of two different pesach offerings. (The P'ri Chadash OC 481:1 writes that this opinion prohibits drinking any chamar medina after the four cups).
The Mordechai (on Arvei P'sachim, 38b) likewise writes that a significant amount of the matzah taste survives even if someone forgot to eat the afikoman. He rules (commentary on the Seder, 34a) that one may drink more wine after the meal is over and the table is cleared, since this does not give the appearance of adding to the mandated four cups. The Bigdei Yesha commentary suggests that the Ran would agree with this ruling.
The Mishna Berura (481:1) writes that it is proper to be stringent on the first night of Pesach and, where possible, to follow all the above opinions. Therefore, he writes, only mild drinks like water, ginger ale, tea, or apple juice should be consumed after the afikoman. The Shulchan Aruch HaRav (481:1) writes that the essential reason for not drinking after the afikoman is to avoid getting drunk, as per the above cited Rosh. Therefore, he writes, one should only try to be stringent on the first night.
Clearly, the four cups of wine instituted by the sages take priority over the objective of not drinking after the afikoman. Despite the Yerushalmi's statement to not drink wine between the third and fourth cups so as not to become inebriated, the Yerushalmi requires drinking those third and fourth cups. Even according to the opinions that prohibit drinking wine because of it's attenuating effect on the matzah taste, the required final two cups of wine that were explicitly instituted by the sages take priority over the gemara's implicit prohibition against drinking after the afikoman. Still, one should avoid drinking more than that and thereby preserve whatever matzah taste survives the last two cups.
I believe, quite frankly, that the question is based on the incorrect assumption that the Sages instituted a prohibition against tasting anything after the last bite of Matzah (which we colloquially call the Afikomen). This is not correct, as can be demonstrated by the simple fact that that's not how the Seder, arranged by the Sages, goes.
The Mishnah Berurah is not telling us that the taste of the Matzah may not be weakened by the taste of anything, but that somehow wine does not weaken the taste of the Matzah. It is true that in many ways a good wine enhances the taste of a meal. There are professionals who arrange formal dinners that pair good wines with appropriate courses of a meal. But that is not what the M"B is about here, in my humble opinion. I think that misses the point of the M"B.
The main point is that the Sages instituted and arranged the Seder. The Seder that was instituted has two cups of wine after the last bite of Matzah. The simple answer to this question is that we are following the Seder. Shulhan 'Orech is over. We have Bentched. But there are still two more cups (and Hallel and Nirtzah) remaining.