Are you talking about the list of events in the component display or in the upcoming events module? The module has a setting where you can set the event to stop displaying when the event starts OR when it ends. The component does not have a setting like that and will display until the event is over.
I noticed this two weekend ago and another person told me the same last Saturday that when they went to look at the attendees so they could print it for the event that evening
The event was no longer listed. At some point on Saturday, prior to the event it must have assumed the event occured. I looked under dtregister and jevent to see it they have a clock setting. I have looked briefly on my cpanel to see if they have a setting but didn't find anything.
The only setting I see is midwest time on the joomla configeration
When the event is removed from the listing is based on the end TIME. So if it ends Saturday at 1:00pm, it will be removed then... even though Saturday is not over.
Based on your article time, sounds like you need to adjust your joomla time setting. Even it it appears to be correct, often times you have to set it different as it is just an offset of your server time setting. Seems you need to bump it one hour. The joomla time is what DT Register will follow.
If you want the events to stay listed for some time after the class is over, then enable "Show Past Events" in the DT Reg configuration. Then any past events that are still published will show. Then you can manually unpublish them when you don't want it to show anymore.