If you select Tapemachine Style and activate the Monitor button (not the Record button), it should never deactivate. Monitoring should remain active at all times in that state, including Play.
If that is not happening, there must be an issue with your particular install or setup. I use Solo Defeat on both the Mix Return channel and it’s Output Bus, Tapemachine Style monitoring with the Monitor button activated as a part of my template. All of that comes up as my default template. It has never failed to work properly.