So, time passes and I'm doing the Beef mission at the Ultra Lux. I'm dressed up as a White Glove, and I have to wait for about 13 hours. When I get out of waiting, I'm told that ED-E and Arcade are no longer my companions, and both have been sent back to where I found them.
I go to Primm, into the Nash shop, and find ED-E and Nash in a shoot-out, and ED-E is red on my radar.
Arcade is fine, I picked him back up and sent him to the 38, so the problem is only with ED-E. Maybe Nash just doesn't like robots?