Apps will often ask to enable push notifications the first time they are run. However how do I change this setting after answering this? There doesn't seem to be a single thing in Settings about Push Notifications. The closest I can find is "Notification Center", but this just appears to customize how notifications appear, not whether push notifications are enabled or disabled for the app. This is a really confusing UI.
There is an "include" and a "do not include" section in Notification Center.
Tap "edit" at top right corner of the Notification Center. This allows you to drag apps around in the Notification Center.
Hold the app you want to stop push notifications from, by the lines on the right hand side to its name, and drag it into "do not include" section. It will automatically close all banner settings for the app, and voila! You are good to go.
So far the only way I've found to do this is to manually choose the alert style for the app in Notification Center. The default is banner, so enabling push notifications requires setting the alert style to banner, turn on badging, sounds and enable in notification center, and similarly disabling all these (banner style to none) to disable.
I really wish there were a single on/off setting for this but there doesn't appear to be.
Update: I got my wish. As of iOS 8 I believe there is now a single on/off switch to enable notifications for an app. This resides in the Settings->Notifications area under the specific app.
If you go into ""Settings" Then "Mail, Contacts, Calendars" Then "Fetch New Data" There's an option to turn Push off and on there, I think that effects all apps since I have some that complain that push is turned off when that option is turned off and they don't when that option is on. I could be wrong though
I had this problem when I wanted to enable push push notifications for my Amazon app in order to get alerts of when my package was delivered or when my package is being shipped. I selected them to be disabled when I first downloaded the app, and couldn't reenable them when I had the after.
The only way I was able to reenable the push notifications for my Amazon app was to delete The app and re-download it from the app store.
Hope that helps...it sucks we have to erase and redownload an app just to enable push notifications.