You could use file options to set a script to run when the file is opened. That script can take the current time and compute the appropriate interval to use Install On Timer to trigger a script that saves a copy. The save a copy script can then reset the Install On timer interval to 24 hours (convert that to seconds) if the file is to remain open indefinitely.
If you hosted the file from filemaker server, you could simply schedule the back up for 10pm.
You could also use a robot file for this where you use CRON (mac) or Task Scheduler (Windows) to schedule the opening of the robot file for 10pm. The robot file then performs the save as script when it is opened.