Aye-aye (Philadelphia, Cincinnati, and Cleveland): No-show at Philadelphia and Cincinnati. At Cleveland, my class trip group didn't have time to get to the Primate, Cat, and Aquatics building where the aye-ayes live. Still haven't seen an aye-aye yet.
Sumatran rhino (Cincinnati): I first found out about Cincinnati Zoo's Sumatran rhinos (and as a result became obsessed with all things zoo) when I was about twelve. Ever since then, I've always wanted to see them. In 2015, news broke that the last one they had (also the last in the Western Hemisphere and captivity in general) would be going to Indonesia to partake in a breeding program there. I talked a lot about how I wanted to go there, but nothing ever came of it. Maybe it could have happened, maybe not, but I'll always think about what could have been...
Short-beaked echidna (Philadelphia): Maybe he was there when I went, or maybe it was a rock. But I wasn't certain I saw an echidna. My luck changed for the better a few years later when I went to the Brookfield Zoo and saw one for the first time.
Brown kiwi (National Zoo, Bronx Zoo): maybe they're always right in front of my face, but I can never really see them no matter how long I spend there. Still haven't really seen a kiwi.