A game could go on for a lot longer period than three months. Someone could be hidden from the ratings even if they are actively playing a game of that type.

Also someone like me who has ratings in lots of different games might not play some gametype for a long time. Even if you are playing actively there are too many types of games to keep on playing all of them all the time :) I wouldn't like it if my rating was hidden from a game i play rarely.