Adding MobiControl agent to battery optimization whitelist
While I don't have any Zebra TC75/TC56 to test out, I've encountered different device models from other brands with similar problem. Have you check what battery optimization option(s) you can configure in your device's "Settings"? In some cases, one might be forced to turn off some or all power-saving mode(s) to prevent the agent from being stopped/killed.
According to the latest v14.2 online manual at https://www.soti.net/mc/help/v14.2/en/scriptcmds/helpindex.html, a new script command "batteryoptimize" has been added for Samsung MDM 5.7+ devices using v13.6 Android+/Android Enterprise device agents. I hope there is similar support for Zebra and other device brands.
I suggest you to open an official support ticket with Soti and see if there will be similar support for your device and agent in the near future. If there is no release roadmap or you can't wait, and you can trust your end-users, you can consider adding MobiControl device agent as an item in your lockdown menu, so that the end-user can, if needed, restart the agent by tapping on the lockdown item.
How are you adding MobiControl to the battery optimization whitelist? With a SOTI Profile or with a StageNow MX setting? Its possible that the application of the LG update (assuming that is performed after enrollment) is wiping out the MX setting? You might want to consider disabling Doze Mode entirely too as we've started to do that in some of our deployments.