Yesterday, I emailed the devs about the issue (and I believe at least one other person did as well). I had not been receiving notifications for incoming attacks, sonar sightings, other player promotions, etc., but I was still receiving the chat notifications. It sounds like we were having the same problem.
Tonight, though, I received a notification for an incoming attack; hopefully, this means that whatever the trouble was, it has been resolved. Let's cross our fingers.
"No man chooses evil because it is evil; he only mistakes it for happiness, the good he seeks."
-- Mary Wollstonecraft