Alright, here's how it went. I asked a question and voted one of the wrong answers down. Sometime later, when I was on the page again, I clicked the downvote button on accident. It cleared the downvote like it should. I said "Whoops," clicked it again, and was informed that I my vote was too old to be changed when I had, in fact, only just (mis)clicked it a moment ago. Is that how it's supposed to work? I'd think that clearing your vote (or even changing it from down to up or vice-versa) would clear the timestamp on the vote as well.
Depends on how long it took for you to register that you had accidentally tried to undo your vote. The warning could have been from the first click but didn't get around to showing you until after your second click.
You can't clear out your vote unless it's within the small window after you first cast. And trying to undo that vote wouldn't reset the time on when you did. Once you vote, that's when it counts.
You can get the vote back if the question or answer has been edited since though.