Ask for Purchase

I'll start with this since recently there's been an issue with ATB notifications not arriving at certain devices. Here's an undocumented possible solution mentioned by several people where editing the name of a device worked for them:

Settings > General > About > Name

Change the name

Then "Done" and retry.

Otherwise If Ask to Buy isn't working, read the suggestions in the document: If Ask to Buy isn't working - Apple Support about looking for the request in Messages or Notification Center.

Make sure notifications haven't been disabled. This article discusses notifications: Use notifications on your iPhone or iPad - Apple Support

and this one Change notification settings on iPhone - Apple Support

Make sure the software is up to date on all devices involved.

Sometimes it helps to have the devices involved take a fresh look at settings:

● Try signing out of accounts and back in again.

Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac - Apple Support

Sign in with your Apple ID - Apple Support

● Restarting is a simple step that can resolve many unexpected behaviors.

iPhone: Restart your iPhone - Apple Support then choose your model.

iPad: Restart your iPad - Apple Support

Mac: Ways to start up your Mac - Apple Support

If a problem persists, particularly over several days, try contacting Apple for assistance:

Click here --> Choose your country or region - Official Apple Support Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

"See a list of Apple phone numbers around the world."

Click here --> Contact Apple for support and service - Apple Support