So, say, because of this issue where you may not have enough time-
If a turn passes by where you could have claimed draw along with your move but didn't get the chance, would it make sense to allow the 'claim draw' flag to remain up for one extra turn of yours following that (being disabled once you choose to make a move), or would that then possibly not be fair?
I think I see what you're getting at- what do you (or anyone else) think should be done, if anything?
There is an unfortunate incompleteness in the draw claiming code in online chess (same in live chess?). As noticed by many people, and verified by rooperi, if you have a position where it is necessary for you to make a move to create a three-fold repetition of position, and you press the claim draw button and then move, you do not get the draw you are entitled to.
It is essential that this order of events work, because it can happen that you create a threefold repetition and your opponent replies instantly, perhaps with a conditional move, breaking the repetition. This leaves no time to press the draw button after you have moved to create the position.