From your description, I know the Microsoft Launcher Android Enterprise Configuration Profile stopped working intermittently.
To troubleshoot such case, log analysis is necessary. With Q&A limitation, it is not a better channel for log analysis. We suggest to open a case to work on this.
https://learn.microsoft.com/en-us/mem/intune/fundamentals/get-support
In addition, share an article for setting up Microsoft Launcher with Microsoft Intune that may be helpful to you to check if the settings are correctly.
https://techcommunity.microsoft.com/t5/intune-customer-success/how-to-setup-microsoft-launcher-on-android-enterprise-fully/ba-p/1482134
Thanks and have a nice day.