I got my answer via email from customer support.
For anyone else wondering about this, if you set your Client Scheduling Limit to Do Not Allow Clients to Schedule Fewer Than to be "0 hours in advance, registration will stay open until the start of the event, at which time it closes.
I have suggested that for those of us offering online events, it would be nice to have the option to keep registration open until the event ends.
I often have at least a couple of people jump onto my events halfway through via the event scheduler I am currently using (which I am abandoning for other reasons at this time).