I had Arcade as my follower for some time, doing quests for the followers, trying to start his personal quest, but no matter what tasks I accomplished, it did nothing. After I parted ways with him only one time, I never had the option to recruit him again.

I have a similar problem; I sometimes lose the ability to recruit Arcade again from the Lucky 38. It does not always happen, but when it does, I have to go back to a save before it stops letting me recruit him. It is not consistent, so it frustrates the feces out of me.

Just happened to me on the PC.