I just bought a new HP laptop ( old unit destroyed). When I went into my music library, music that has been recently purchased with my ipad is not in my library on the laptop. I deauthorized the old unit and authorized this laptop. The recently purchased music still doesn't appear in my libary. Why is this? Any time I previously purchased music it always appeared on both devices.
New purchases will download automatically when that option is set, but not past purchases unless you sync them from your iPad or download them from the Purchases area in the iTunes Store. This user tip from TuringTest may help:
https://discussions.apple.com/docs/DOC-3991
as well as this page on "How-to Geek":
http://www.howtogeek.com/104298/sync-your-ios-device-with-a-new-computer-without -losing-data/
Regards.
New laptop
