I don’t know about that particular carrier board, but in general a battery backup would be needed for longer duration shutdowns. The traditional way of dealing with this on carriers without battery backup is via a supercap.
There have been some past posts on other boards of how to connect a battery backup, so I suspect there is the same possibility on your J120 (I don’t know what it would be though).
As a workaround if you have network access you’d want to enable NTP (network time protocol). I am assuming that if this is on a drone or robot type device you won’t have outside world networking available, but if you have a Linux host available during boot of the drone (e.g., via WiFi), then the host could forward its time and date information via NTP and have the Jetson set its time from that.