Dave:
I had the same condition a while back with the engine shutting down casue the UAT was empty and interestingly the Main tank feeding the UAT half full !! Was quite puzzling.
What it was is the UAT itself was sucking air AROUND THE CAP because it was one of the early ones that did NOT have the Teflon tape on the threads !!!! This was pointed out to me during the investigation by none other than SWB themselves who developed this technology and make these things.
SO, it may be several other things as previously mentioned but it is worth spinning the cap off the UAT and replace the Teflon tape with a generous amount if you have any to start with.
BR