I was also having same issue before but its now solved after done the following, i am using 720 & 920.
Chk this in Settings:
1. Settings -- Application --- Back Ground Task: Whatsapp should not be blocked to run in Back ground App
2. Data Sense -- Settings: Uncheck ?? Restrict background data when i am near my Limit??
3. If you run battery saver mode then you have to deactivate it: Leave Battery Saver ON, in Advance Settings select Conserve Battery: When Battery is Low.
Give a Restart or Soft Reset (Vol. Down + Power) might give a solution to your problem.
That doesn't work for me.
Tried both, enabling and disabling background task; I don't use data sense, and I also don't use battery saver mode. And of course I've done some proper reboots and soft resets. Everythings is still the same.
I still think it's whatsapp's issue with push notifications or microsoft's fault with their push notificaction system.
I don't use Line or WeChat, but, maybe we should check with the users of those Apps, if they have similar issues; then we might get an idea of what's behind our troubles.
Cheers. And hope we all get a solution, cause really, WP is worth it (at least how I see it).