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Since the Trope Repair Shop is full, I guess I gotta ask here. This trope seems to encompass several factors that are getting mixed and matched in the examples:
I think the key phrases are "only you" and "repopulate my race". Both need to be present to be this trope. Therefore Superman and Maxima, among other examples, don't belong. Maxima just wanted a strong, handsome mate. There weren't any indications that an Almeracian (that's her planet, Almerac) man wouldn't have been able to father her children just as well.
We may need to split the "we need more genetic diversity" and "we need more people, period" examples into their own tropes.
Does it have to be limited to one fertile male and/or one fertile female? There's an example from Greek Mythology of the Argonauts stopping on the island of Lemnos. Due to a local Gendercide, all Lemnians are women, and they want all the Argonauts to have sex with them so they won't die out. (Somewhere along the millennia, Lemnos got confused with nearby Lesbos, and "island of women desperate for fertile guys" turned into "island of women who only love each other," giving us the word "lesbian.")
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How well does it match the trope?