There is a general requirement in Cute that you must introduce yourself to a character before you will be able to experience any events with him/her. Skye is one of the few exceptions as his First Heart Event introduces him. Even so, if you have not introduced yourself to Lumina, Skye's First Heart Event will not trigger.
In my own games, I always meet every character within the first or second day of the game, so I never had any problem triggering Skye's First Heart Event. It was only when a player wrote to me to say that the event would not occur for her that I realised a prior meeting with Lumina could be a requirement.
In fact, this was the case. When I suggested it and she tried it, the event occurred without any problems.
This information will be added to my guides for Cute, but for players who have had the same problem, I thought a post might be in order.
It does not really amaze me that most of the emails I am receiving about Cute ask about Skye. The Harvest Moon fan base is mad about Skye, but then, so am I.