The other day I forgot to say Aleinu by Mincha. After Maariv I asked the Rabbi whether I should say Aleinu two times (one for Mincha & one for Maariv) and he said in my situation one only says Aleinu one time. So that got me thinking - say someone forgot to Daven Mincha, he Davens two Shemona Esreis by Maariv. See SA OC סימן קה in the Mishna Berurah. Why is Aleinu different than repeating Shemona Esrei if forgotten, where we do a makeup Shemona Esrei but not a makeup Aleinu?
Shemonah Esreh is tefilla. As such, if you miss out by mistake, you can repeat to "make up" your obligation. Saying Aleniu at the end of tefillah is purely minhag, and it is not part of the rabbinical/biblical command to pray*three times a day. As such, the obligation of tefilla, which mandates the repeating, is not really relevant.
*a discussion for another place