This happened to me after I had to reset the device and it turned out the Screen Timeout was set to 1 minute. Drove me nuts until I discovered what was wrong. The device was probably reset before you received it.
To fix it, tap on the gear in the top right of the screen (to the left of the battery indicator) and click on More..., then click on Display and change the Screen Timeout to 30 minutes or something.
I have no password on my router either (live on top of a mountain) so that should not be an issue at all. My KF works fine.
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