I have run into some instances where you cannot get an achievement anymore, but they aren't disabled.
Nuclear Dawn has some time sensitive ones, such as killing a Developer in a certain year. There aren't that many people on these servers, so it is difficult to even know if a dev would show up and/or if you would get the achievement if you killed them. Killing Floor has time sensitive achievements also, but it is only on the description. For example, there is one to get an achievement killing various Christmas themes monsters (I think a Santa also) at a specific time in the past. But you can get those at any time now if you play on the Christmas map.
Red Faction: Armageddon has a bunch of achievements for the co-op Infestation mode, where you just kill waves of enemies. The matchmaking is non-existant and I have never seen any other players on this mode. The mode or maps themselves are difficult to play by yourself. You will die a lot this way. But it seems possible to get all of the achievements in this way, playing by yourself in boring game and dying all the time. But then since there is never any other player to play with, you won't get the revives achievement, or the 4 player one. Strangely, the other bonus mode (Ruin Mode) has no achievements at all.