The documentation for animate() explicitly mentions:
Because of the nature of requestAnimationFrame(), you should never
  queue animations using a setInterval or setTimeout loop. In order to
  preserve CPU resources, browsers that support requestAnimationFrame
  will not update animations when the window/tab is not displayed. If
  you continue to queue animations via setInterval or setTimeout while
  animation is paused, all of the queued animations will begin playing
  when the window/tab regains focus. To avoid this potential problem,
  use the callback of your last animation in the loop, or append a
  function to the elements .queue() to set the timeout to start the next
  animation.
So, you can either call setTimeout() in the callback of your animation to chain the next cycle, if possible, or queue() the calls to setTimeout() between the calls to animate().
EDIT: As requested in comments, here is a simple queue() example. The code below enforces a two-second delay between the slide animations:
$("selector").slideUp("slow").queue(function(next) {
    window.setTimeout(next, 2000);
}).slideDown("slow");