I just received a new Z3 from a cousin...and having pretty much the same issue....sigh!!!

While on Wifi, my whatsapp does work...I had to use the browser to surf and only then the phone connection to wifi is established, else the whatsapp msg would be sitting with a clock sign

But at some places....(my friends house), it seem that the wifi is auto connected and is ON all the time, but when I come back home, the connection is not established unless I start to browse.

I have other phones, on android, IOS, and nokia which are working fine