My iPhone's playlists don't appear in iTunes

When I connect my iPhone 5 to iTunes, under "Devices", my iPhone's name appears and if I click on the little arrow beside it a list drops with "Music", "Movies", etc and right after "Tones" there are some of the playlists I created on my iPhone. However, the most recent playlists I created don't appear and if I try to create a playlist on my iPhone right now and then connect it to iTunes the playlist won't be there. Here's the thing, I want to sync my iPhone to iTunes but don't want to have to create those playlists by hand again.

Question 1: is there anyway to solve this so that I can see new playlists on iTunes and then export/import them?

Question 2: if not, is there any other way of exporting the playlists from the iPhone and then import them to iTunes?

Thank you