I've actually heard of this happening before. Just play until it really dies! :)
My Xbox is 4 years old, and recently it takes longer to shut down. Otherwise it still works!
I've noticed this too with one of my old fats ever since the update. It's not a ridiculously long time but it used to be instant.
I LOVE paying for Xbox Live! I also love that my love for it pisses off so many people.