In the campaign I've been playing, I've captured two Mk V Fabricators (Zenith Chameleons, and something else that I can't remember offhand). In both cases, I set them to start producing units. When I checked back at that system some time later, I found the Fabricator no longer present, having produced a nice set of units.
The first time, I just chocked it up to the Fabricator getting sniped in a wave, but the second I deliberately put a Mk III forcefield around the Fabricator, and it was still intact when I noticed that the Fabricator was gone.
Are Fabricators supposed to disappear for some reason?