What causes continuous rolling thunder when no lightning visible?

Electrical sparks still pass through the cloud above its dense mass. Only some of the charge hits the ground.
A lightning storm is an awesome sight from an aeroplane

The lightning is still there, it doesn’t always light up the sky, even at night. Much of it is the lightning going on above and between the clouds when the cloud base is thick enough to hide the flash.

Could be cloud to cloud lightning obscured by the cloud deck, or even cloud to ground if there is a great deal of low cloud and rain between you and where the lightning strikes are flying. But that sort of phenomenon wouldn’t normally produce a continuous tone.

If you hear a continuous roar in a approaching storm, best take cover. It might be a line squall with some extreme straight-line winds, a wall cloud or worse, a tornado coming. I’ve been through an F1 and even that made a hideous roar as it closed in. It lifted from the ground a couple of houses away from my house, then dropped back down a few hundred yards beyond us and ripped through a wooded area twisting off huge oak trees from their trunks. The big ones like F4 or F5 are loud beyond belief.

If the lightning burst is away from you, expansion pulse along the arc will arrive at your ear at different times. For example if the arc is cloud to cloud, away from you, and and is about 2 miles long you will hear the rumble for a duration of 2 seconds. The closest portion reaches you first, while the sound from the rest of the burst continues to travel to you.
People located perpendicular to the burst will hear it as normal thunder.
Try the experiment and call your friends. Ask what they heard. You can even do this to determine where the lightning was located.

Valid points are mentioned in all previous posts. Nobody, however, identifies reflected sound as a source of continuing rumbles. Much of the tail end of a single thunder clap consists of sounds bouncing off distant hills or other sound reflecting features of topography.

The fact that the initial sharp crack degenerates into a lasting low rumble would indicate that the highest audio frequencies are readily absorbed by reflection while the longer-wavelength low-frequency rumbles are not.

Laws of physics.