I had an issue with my second adoption where the adoption agent showed up, but not the pet. After testing it turned out something about the lot was bugged and preventing the pet from spawning (or staying spawned- on one trial the pet did show up but disappeared before my sim could interact). When I mean the lot was bugged I mean just that instance - in a new game, the same house/lot worked fine; also, the same sim moving to a different lot worked fine as well.
I worked around it by having my sim temporarily move to a blank lot, adopt his pet there, and moved back to the original lot.