Root veggies like beets, carrots, parsnips damp off pretty easily. That could be the problem with your beets.
One observation: some of the vegetation looks light green, maybe it's the lights? Or it could be overwatering, the soil looks very wet.
Looks like a fun project.
I'm done with the veggie tent concept myself.
The ROI was too low except for cukes and chilis in my case.
But you have got me thinking about a simple set up for greens and herbs ... and come Spring ... veggie starts.
Then I can keep 2x4 tent for chilis and the 4x4 for cannabis.
It's both. It's the LED lights combined with a bit of over watering. When I'm dealing with these cardboard pots before they go into their final location I'm dancing a fine line between too dry and too wet. So I leave a quarter inch on the bottom of the tray for the roots to get to. In some cases it's too little and in some cases it's too much. I'll stick with the plants that do well in that style of care unless there's a particular plant that I really want and then I'll pay closer attention. I'd rather have the attitude that any of them can die and I'll have plenty left to work with then care too much about an individual plant or individual type of plant.