Beacon transmitters can only keep going so long as the app that creates the keeps running in the background. If the app stops for some reason (the operating system kills it, the app crashes, the user force quits it) the transmission will stop.
The most likely cause of the problem you report is that the operating system is killing the app for some reason. Motorola devices are usually pretty faithful to open-source Android, so it is a bit surprising that Motorola devices are doing this. On a Pixel 7a, I often see beacon transmitters running for many days at a time without stopping.
There are many techniques BeaconScope (and other apps) use to keep running in the background: (1. Broadcast Intents, 2. ForegroundService, 3. Job Service). The latest 1.5 version of the app uses 1 and 2, but not 3. I added this to version 1.5.2 of BeaconScope just now and sent that for review in the Google Play Store. This should be available in a couple of days, and it may improve things by restarting the app within 15 minutes if it is ever killed by the operating system.
If you would like to help troubleshoot why your phone is killing the app, so I can make this more robust, I can give you instructions to do one of two things (1) Use Android debugging tools to get an app log - this requires installing Android dev tools (2) Sending a bug report - this requires performing a procedure on your phone within 60 seconds of when the transmission stops. Let me know if you can help with either of these and I will share instructions.