It would be helpful to have a message notifying one when the limited time quests have reached their limit for a character. Perhaps the quest information text on quest givers could also show that it's limited time, and how many tries there are.
Unless I'm missing something, currently the only way to know is to go for the quest only to learn that pc can no longer do it.
If scripting something like this takes too much time, the max limit on the quest giver + efusl gives everyone exactly what they need. Doesn't really matter in the grand scheme of things however.
I see no reason why not.