Yes, it's strange. You need a point in time (not a period of time) after "since." Try, It's been so long since a new day began/dawned. Even that sounds strange!
Thanks! By "new day" I mean to say 'moving on' or 'letting go' after the end of a relationship. The whole song is about nights and days.Does that make more sense now? And anyhow, you say that I don't need has/had at all in the sentence?