For all intents and purposes, you end up being penalized for pausing the game when you aren't actually playing it (even though a tip that appears on startup recommends that you pause the game if you're going to be away a while).
Even if you do remember to check the log to try to work out what time the next event is due, if you actually happen to have something else to do that prevents you playing at time, then goodbye to that event. And after that, there never seems to be any indication as to when another event will be triggered, so you just sit and hope you'll see one again sometime in the next few days.