To trigger special events the next day, you must accumulate enough Love Points while playing in "Mode History" (on any difficulty level, excluding "Mode End").
Your first major milestone is 300 Love Points, which will start unlocking special events. However, don't stop there! The more love you gather from that point onward, the more events you will unlock. Keep fulfilling her needs using the yellow cross icon in the actions menu and never stop building that affection.