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Sometimes the Xperia Z1 phone disables my WiFi without asking me. I just discover that when I check the phone and find the WiFi sign off. The problem is I don't want it to disable the WiFi under any circumstances.
Note: I noticed that with my previos ACRO S phone but I thought it is only a problem with my phone hardware or something.
Do you have the option "Keep Wi-Fi on during Sleep" set to always? Settings/Wi-Fi/Options (3 dots)/Advanced.
Another option is Power Management/Stamina Mode. If this is enabled it will disable Wi-Fi when the screen is off.
Sounds like Stamina. You can alter its behaviour to allow for lower battery levels before it intervenes