I don’t have a good estimate unfortunately. I spend about 30-60min on a working day trying to keep up with all things related to mybinder.org. This includes a lot of different stuff: checking on the deployment, admin tasks to move things forward, admin tasks to repair stuff, checking chat/forum, thinking about stuff, evangelising for mybinder.org, PRs on the various project project binder works on (BinderHub & repo2docker mainly, zero2jupyterhub sometimes, kubespawner, various notebook extensions rarely).
Without wanting to tempt fate the actual day to day operation of mybinder.org requires very little effort. Most of it repairs itself through restarts. Usually day-to-day stress comes when we add new features or otherwise (try to) improve things. The time between failures/events that require attention is probably “a few weeks” now. Every time we add a new cluster it goes down to “a few hours” until we overcome the growing pains for that cluster.
Usage on mybinder.org has gone up significantly now that university term has started again in Europe and the Americas. We are seeing more traffic than before so I suspect we are in for some more growing pain soon (but I don’t yet know what it will be ).
In summary I’d say operating a “not brand new” BinderHub deployment on a good quality cloud provider like GKE takes a few minutes per day of checking things over. If you want to keep up-to-date with new development you need a bit more time to understand how risky an update is (can I apply it before lunch or do I need to be available for problems?). The way to do that is to spend time engaging with the various repos and their day-to-day (potential to spend an infinite amount of time on this but generally the speed is low).