Meanwhile, I've tried a few more things.
Uninstalled from the iPad, test on iPhone, nothing.
Log out/in on iPhone, still nothing.
Uninstall/reinstall on iPhone, still nothing.
Reinstall on iPad, start getting notifications on iPad, WITHOUT even opening or logging in on the iPad.
Updated to v2.12.33 on iPhone and iPad.
Still only getting notifications on the iPad.
Tried logging out/in on iPhone, still only get notifications on iPad.
You should try not upgrading both;leave one on a older version.
Updated to v2.12.37, but still no notifications on iPhone.
Same problem here. iphone 4, OS 7.1.1
Upgraded just the iPhone to v2.12.40, iPad still at v2.12.37, but no notifications received on iPhone, only iPad. All moves made from the iPhone. Also logged out/in on iPhone between first and second move, but that didn't help.
Same problem on my iPhone 5s running ios 7.1.1
My friend lost a game because he thought I didn't move... Effientcy people!
On v2.12.40, still not fixed, iPhone 6.1.6, iPad 7.1.1, only getting notifications on iPad.
Same here, for iPhone 5s and ipad 4
This just started happening to me yesterday iPhone 4 ver 7.1.2.
Very frustrating ! I've even factory rest the phone !
I am having the same problem on the iPad. The notifications are working on my iPhone.
I tried to deleting and downloading the app on iPad. No luck!
Does anyone have a resolution to this?
iPhone 5s, all software updated but the same issue. Notifications not showing up on the app icon. Very frustrating!
Same problem with iPhone 6 and the past several versions of iOS. Currently running iOS 10.0.1
ive been back and forth with support. They tell me they're working on it but no success yet.
Hi there,
Since reinstalling chess.com on my iPhone and iPad, I haven’t been able to get notifications. So frustrating! In the notifications option under ‘Settings’, chess.com doesn’t appear either. Can anyone help?
Best,
Lydia
Wel that won’t work - I just traded in for a new iPhone X (iOS 11.1.2) and no longer receive the badge app notifications. 
All notifications were turned on in the settings on the phone I had before and it usually worked. I tried reinstalling and on the new phone Chess doesn’t even show up in Notifications as an option. (Also doesn’t show up as having any Settings except Siri and Cellular Data, plus the in-app ones - not sure if that’s normal. There is no option for background app refresh for this app either.)
My old phone still gets them over WiFi (when I power it on) but the new one gets nothing unless I open the app (at which point the badge shows up if I back out before making a move). Nothing showing in Notification Center history either - looks like the phone hunks Chess just had no notification integration.
Any help much appreciated!
I have this problem. iPhone 3Gs iOS 6.1.6, Chess.com iPhone App v2.12.28
Tried logging out/in, then rebooting the phone, then uninstalling/reinstalling app. Still not getting notifications.
However I am getting notifications on my iPad 3 iOS 7.1