The game does give you a little leeway, if they "reverse" on you and you tell them "no" but they say they'll leave anyways (or if you say "yes" and they decide to stay). If you visit their house the night before they move, you can usually get them to stay then......Isabelle will always tell you when you start a game that someone "is moving tomorrow" and urges you to say good-bye. So even if you can't play often, if you at least start it up, you'll know when people move in and out! XD

I've also noticed, if you tell someone "no" and they say they'll stay--it'll be about 2 days before it generates the next person who'll say they're leaving. :) Sometimes, also the mailing list (you go to write a letter) will be ordered in that the top of the list is most likely to next tell you they're leaving. It is fun, though, to watch the credits (sit on the large tree's potter-bench) and you can see when your "current residents" moved in--exact day and time. :D