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 hadn't noticed this until someone else brought it up, but same here. 4.5 year old Zephr model used to shut off almost instantly but now I can hear the fans spinning for a good 20 seconds after the green power light turns off. It's definitely from the update.