Not really. They appear a couple of times early on in a game, then once a day after that. If the game isn't opened for longer than a day, only the one event will occur. There is another way to get an extra event, but that depends on a random event itself. Mouseover below for a spoiler:

When the Gong is struck, sometimes it "grants luck". A few minutes afterwards you will get an extra event.

END SPOILER