I'm having exactly the same issue. I'm using a 2012 mac mini on Mojave with Logic Pro X 10.5. I know it's an old computer so as it worked fine I never update anything on it, Logic Pro X, or the audiobox USB 96. Also I rarely have more than 4-5 tracks in a Logic project.
When I turn everything on it works for a little but then the sound and monitoring just stop. Usually after I listen to a track and stop it. Sometimes it actually sputter out and stops
If in logic I switch the output and input device back to built-in input and built-in output it works (Logic Pro X --> Preferences --> Audio) but that's no good to me.
Is this just a faulty device? Any ideas?