Hey there!
My last girlfriend was almost exactly like this. She'd usually be in an upset/depressed/quiet mood.
I usually find women like this to have some depression issues, however.. This is only a minor detail you mustn't worry about.
Women of this sort are usually more emotional, need Comfort, optimism. They need to feel loved much more than other girls you might have been with.
Take control (alpha male trait), ask her if she wants to do / go to something at whatever date (just set a date, and if it doesn't work for her, she'll let you know when she's free).
When they're "sad and don't really know why anymore". It could be some sort of remorse, or mixed emotional display of an old boyfriend they don't know how to feel about now.
Take her mind off of that, by showing what an awesome guy you are.
Make sure that your emotional connection with her is better than your rapport connection. Otherwise, you'll seem AFC.