I'm pretty sure Reinis Rex went to Adventure Camp once and decided he didn't like it.
Reinis just didn't like going out much. He got separation anxiety from his Uncle Richard until his teens, and he was terrified of forming any attachments in fear of being abandoned again. (In many ways he and Buddy had the same issues, but unlike Buddy Reinis never overcame his separation and social anxiety.)
I don't know what specifically caused Reinis to decide he didn't want to be at Adventure Camp. Like Annie he definitely struggled with "overbearing city rules," but maybe there was a predator attack during that one trip he was on that made him feel unsafe enough to never go back.
Richard had wanted Reinis to at least try Adventure Camp, but he wouldn't have pushed him to try again. Hence him only going once.