I have a similar problem,  but I'm not rooted nor do I use any task killers.

In my case,  it seems that my Wifi goes to sleep with the device and when it wakes up it seems that the Wif is ON (bases on the notification icon),  but the wifi wont work unless i toggle it OFF and then ON again.  Then I'm fine until the device goes to sleep again.

(And yes, My Wifi is set to be 'always on')

Has anyone else heard of or experienced this?