LOLNO.
Threefold Repitition

"At move 16, I could have played NxQ, which would have put me up 8 points in material and given me a mate in three. Instead, I chose to castle kingside. Now, ten moves later, my opponent is threatening mate in two. Can I still play NxQ?"

That's a flawed analogy. I'm asking about the limitations of the threefold repitition rule in chess.

Nevermind, I've found the answer. My last attempt at Googling was unsuccesful.
No need to be rude, Artch. What made me wonder was that I know if an opponent offers a draw, you can accept it at any point in the game, even if you're about to be checkmated.
For over-the-board games, you can only claim it when either (1) your opponent has just played a move that creates a threefold repitition, and you have not responded, or (2) you can make a move that creates a threefold repition, in which case you write down that move, then claim the draw.
Similar for internet games on servers that do not automatically end the game when there is a threefold repitition, although I'm not sure how they handle the second part.
The rule is similar for other draws that you have to claim, such as draws by the 50 move rule. If you do not claim the 50 move draw, and then later a pawn is moved or piece captured, the count starts over.
No need to be rude, Artch. What made me wonder was that I know if an opponent offers a draw, you can accept it at any point in the game, even if you're about to be checkmated.
In OTB play, a draw offer is only good until you accept it, reject it orally, touch a piece with the intent to move or capture it, or the game ends in some other way (for instance, someone's flag falls).
The rule is similar on most internet chess servers, except oral rejection is either replaced by a reject command or button, or dispensed with.
To claim a draw by threefold repitition, does it have to be the current position on the board that's been repeated, or can you claim the draw later on? In a recent game of mine, my opponent (or I) could have claimed a draw by repitition, but chose not to. A few moves later, I found myself facing an unstoppable mate in one. Could I have claimed a draw?