Is it inappropriate to reply to questions that have had no activity for some period of time?
If so, why, and what is that period of time? (The noticeable upvoting of the first comment to a recent answer leads me to ask this.)
if there is no accepted answer for the very old question why someone couldn't give a better answer to this question, obviously everyone would benefit from this, users which found question by searching, and the one who answered by growing reputation
I think that if it's a fine question that just was unanswered, or did not have a satisfactory answer, and you are sure you have a correct or better answer, then I think it's perfectly reasonable to answer it. People reading the question will learn something, people searching the site in the future can come across it and profit from it, and there's even a chance the original asker will still come back and read it and gain something from it.
But I do think the standard for answering inactive questions should be higher than usual... if you just have some partial answer or idea how to do it, probably it's not such a good idea, as currently the turnaround time for the main page is just a few hours and this might help get current questions lost.