Isn't there a CMOS battery in Xbox 360 to preserve date&time setting?

Solution 1:

To answer the title's question, no, there is not. Google's opinion (for instance, the post here, waay at the bottom) is that there's only limited ability for the xbox to retain real-time date/time tracking; at best it can last 12 hours when unplugged, at worst 45 minutes. Since you said you turn off the UPS every night I bet that's what's happening...try leaving the power connected for a night and see if it does the same thing. Posts also abound claiming that as long as you're connected to XBL it should auto-update the time on boot.

Solution 2:

The Xbox 360 does not contain a CMOS battery, no. The RTC chip on the xbox is powered solely from the power brick (which will continue to draw small amounts of energy while the box is powered down, for WoL, RTC and a few other features).

My advice would be to look into some way to turn off the warning noise on the UPC - it should be possible to turn off the noise, allowing you to get some sleep while also keeping your devices safe from power failure.