The device might be rebooting due to a power issue with the wall or the power supply.

Can you run an extension cord or move the device to try a different wall outlet for a while?  If you have another Network Extender then try swapping the power supply and cable to see if the problem follows the supply or stays on the current device.

That being said, a 12 hour reboot sounds like a scheduled task from something.  Someone might have setup a UPS power cycle that is impacting your Network Extender.  Try to monitor and record the times of the outages and look for patterns.

If the extender reboots at the same time of day it might be due to some other device interfering with the power.  For example if someone runs a microwave or another device that draws a lot of juice.