This is only true for the red and blue lines though. And since they only have one track for each direction they must interrupt the service to do maintenance.
It depends on where in the system the maintenance is needed. On the Blue Line they just have the trains share a single track for a while while work is being done on the second track. On the red line, they do the same thing outside of downtown. If the work is being done downtown, the Red Line trains can use the Pink/Green/Orange/Brown/Purple tracks and go elevated instead of underground.
Chicago's subway is 24/7, too.