I did a test, and I am unble to see the kids when I sent them to archive. I also, at some point, lost the option to retrieve ANY of them. Please note, this was all on the same hour of the same day, without even laying again with the mothers..Please do fix this.
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So you didn't have sex with the mothers, but you still got kids, who were all born in the same hour, and now you don't have the "Find Kids" option in the Nexus?
Sorry to say, but if true then that's a result of you or someone else messing with the game variables, and not an issue with the game.
If kids get sent to the Nexus then the option to see them and retrieve them are the same - you click on "Find Kids" in the bottom-left of the Nexus navigation and then type the name of the kid you're looking for.
Are you sure the kids aren't in the daycare at the farm?