Yes! I'm having exactly the same issue, and it's driving me nuts. almost no apps notify me in real time. Examples are: Whatsapp, tinder, Pushbullet, Facebook Messenger. This is really annoying, I hope there is an fix!
EDIT: Appearantly, it's even worse. When the screen goes off, after a while, it seems the whole internet connection is broken off. I tried sending an email, , a pushbullet message and a Whatsapp message (Via Whatsapp web) and none of them worked directly. Whatsapp web also gives the error that "The phone isn't connected to the internet"...