Default Google Services Framework missing or google account not configured (PUSH problem)

Hello,
I observe this problem already longer time, push notifications are not delivered to my phone in time. I see this on many applications using Google push notifications. The push events only deliver on regularly scheduled synchronization events (ie. actively requested by phone)
Today I'm trying to bind Pushover application (https://play.google.com/store/apps/d...block.pushover) to my online account. After filling in the ligin details it popups message

Error
Your device doesnot appear to have a Google account configured, which is required for receiving push notifications, or the Google Services Framework is not functioning properly.

I have google account set up (Settings -> Accounts and synchronization (ON) -> Google account email -> all checkboxes are ON)
Google Services Framework version 4.0.4-430453 (com.google.android.gsf) is present in my phone as system application, not frozen

I need some clues what's wrong