The general rule is that if one inadvertently neglected to daven, he may fix his error by adding a second Shemoneh Esrei in the following tefillah - as is well known. Mussaf is the exception to the rule, and one who misses it has no recourse. Just to feel really guilty until Yom Kippur😊.
Rav Soloveitchik explained the reason being, based on Tosfos in Brachos [26a], because of the general principle that korbanos may not be offered outside of their allotted time [avar zemano bateil korbano] . While this is true as well regarding the korban Shachar, which corresponds to our Tefillas Shacharit, and the korban Bein HaArbayim, which is the basis of our Tefillas Mincha, so no tashlumim should be available, but since there are other important themes in those tefillot, [Berachos 26b] a tashlumim is possible. Even if the aspect of u’neshalma parim sefaseinu is lost, nevertheless, a tashlumim is worthwhile because of the other themes. Only of Mussaf, where u’neshalma parim sefaseinu is the primary motivation for the tefillah - to Briskize it we can say that ונשלמה is the עצם חפצא of the תפילה, would we say that having forfeited that element of the tefillah, there is no longer any purpose to daven at all.
