I assume you are turning off Wi-Fi completely, not just disconnecting the device from whatever wireless network it's connected to, right?
This does sound a bit like the machine is trying to run its own show, but we can show it who's boss. Let's do a Master Reset to restore the factory settings. This will not undo the update, it'll just realign the bits that got out of whack and remind that device that you are in charge here.
Before you reset the device, let's backup some crucial information. Use this link for that: http://support.t-mobile.com/docs/DOC-4866#Back_up_device_files_to_computer_before_master_reset
Then, you're ready to perform the master reset. Here's a link for that: http://support.t-mobile.com/docs/DOC-4866#Master_reset
i want you to turn off your device
when off press and hold the power button
while continually pressing the menu key
if done correctly your phone will boot into safe mode
from there see if you have the same issue if you do do a Master reset
if you don't it was an application causing the issue and you just need to find and remove it
Well, since I've only had this for a week, I don't mind the master reset, so that's done, and I'll let you know what happens.
When I google this problem, two interesting items pop-out.
On Sprint Note 2's there is a package called the Connection Optimizer that seems to cause this, and there is a setting to turn that off.
On the AT&T note 2, there is an auto connect setting under advanced settings in wifi.
But though the same behavior is occurring to me on T-Mobile, there is no setting to turn it off.... Makes me wonder if T-Mobile took out one setting too many.
ALSO, I do find under WI-FI Advanced settings, a checkbox titled,
Check for Internet Service [ ]
Check if wi-fi internet service is available when connected to AP
The default for that is off. Can you tell me what turning that on does?
Sprint has a problem setting that keeps turning wifi on called Connections Optimizer
AT&T has a problem setting that keeps turning wifi on called Smart WIFI
Verizon has a problem setting that keeps turning wifi on ( Settings>Wi-Fi> (menu button) advanced>uncheck Auto-connect)
I am a bit worried that T-Mobile has the same problem, but no way to turn it off....