The problem (to me) is clearly an issue of Anope interacting with UnrealIRC in a latent response. Anope informs the client that they have been authenticated, and then Anope informs UnrealIRC that it should +r the user.
I informed #anope on irc.anope.org that they should perform this operation in reverse -- first setting the user +r and only then informing them that they've successfully authenticated, so that clients can react to NickServ "Password accepted" messages.
A work-around would be to add an N second delay to reacting, or add a behavior for UnrealIRCd to check for "* NickServ sets mode: +r" messages instead.
