I have worked with a somewhat similar setup to what you're describing (aprx stored in a network drive that was left open overnight while processing data referenced from a cloud-based server) but I did not have an issue with the arpx freezing when attempting to use the aprx the next morning. Perhaps the issue here could be backups being created of the network drives that breaks the connection to the aprx or the data at some point in the middle of the night?
To troubleshoot, you (or the other user) could create an aprx that is stored on the machine instead of being stored on the network. If the process works without issue, then the problem could be using an aprx that is stored on a network drive and not the data being referenced on the network drive.
If the original aprx being used is already stored on the machine, then this could narrow down the issue to the loss of connection to the network data and not the functionality of Pro itself. To verify, create an aprx not connected to network data (you can create "fake" data that's only stored in the project database) and then allow the machine to keep the aprx open all night and see if there are issues with the aprx being frozen the next day.
