Hi @SophiaLatini,
I haven't noticed that these indicators ever go away, but at the same time I cannot find an old example to check on in my Canvas (as discussion post editing is a super rare thing to have happen here). If you could link to any documentation you found saying the indicator would go away, that could really help. The student guide specifically says: "Canvas displays an Edited by label on the edited post. The label displays your name and the date and time the post was edited. This label cannot be removed." That statement should also apply to instructor/admin edits as far as I know.
P.S. You're right that the timestamps for discussion posts/replies seem to disappear from default view at some point, but if you hover over the date, you'll see a tooltip come up showing the full date/time. Canvas is generally very good about retaining information in its databases, even if it's not necessarily displayed.
-Chris