Stop a villager from moving, and then just quit altogether. Nobody will move out, I recently have rebooted ACNL for the Fair challenges and before that, I haven't played since early October.
This isn't a Tamagotchi you know.
Just kidding. I don't think there's any way you can stop the time. The only thing I can suggest is logging on at least once every two days to check on your animals. It should take 5-10 minutes max, you could probably do it before going to bed.
I don't know just how tight your time schedule is though.
EDIT: FireNinja's method probably works! I forgot that you could do that.
You can freeze the time in your game by jotting down the day you are at right now into your 3DS notices (that yellow pen in the home menu). Every time you want to play just load the game on the same day you played last.
Other than that, the only thing you can do is time travel to catch up on events that you may have missed and things like that.
I know how you feel because there are times when I don't play the game (I'm no longer in school so it's not because of that, though) because I'm too busy and tired. Sometimes when I have 10-20 minutes to spare, I'll enter the game just to check on my villagers and run some quick errands.
This is pretty much what I do. I check on the weekends! But understanding that you're somewhat obviously too busy for that, I recommend FireNinja1 's suggestion. And don't be scared to make a comeback after a few weeks! The more you wait, the worse it gets, so keep that in mind u v u
I hope that no one you love in your town ever decides to move out n u n) ♥