08-03-2013 20:16 - edited 08-03-2013 20:19
Make sure you have settings>WiFi>advanced>keep WiFi on when screen times out enabled otherwise once the lockscreen comes up, and you are not on a charger, WiFi disconnects and you switch to your mobile data connection.
Click on the blue Star Icon below if my advice has helped you or press the 'Accept As Solution' link if I solved your problem..
I too had the same problem on my LUMIA 620.
Got tired of this problem and always overran my data limits.
Then I did something illogicaland and unchecked the "WiFi always ON" control and that kept WiFi ON all the time.
Checked the box again and the WiFi started going off.
Now I keep this check box unchecked and everything is sweet.
Looks like on my machine the instructions are working in reverse.