Tridion sites 9.1 - the Business Process Type (in publishing tab) is from time to time switched to 'None'

I faced the similar issue recently and that was because of the content import (using content importer or using import export service). You can check if there is a content porting activity that happens just before Business Process Type is set to "None". If that is the case then make sure you exclude the BPT from the export package.

This happens sometimes when you export the entire publication with all dependencies and import them to a higher environment as well.

Check each Publisher Topology Manager weblogs for all your publishers in case one of your Topology Managers is going offline periodically.