Timely question. I have the same issue. (2001 "34 Limited) Been working like a champ forever then all of a sudden today, nothing. Did a little investigating and checked behind the hose connection. There is a spring loaded O-ring "stopper that appears to be there just to stop water from siphoning back out the flush connection. (certainly NOT the issue) That was about as far as I dared disassemble as we are leaving for San Diego tomorrow. I did break out the manual and tried to decipher the plumbing diagrams that came with the Airstream, but they are a bit confusing and dont really seem to match our setup anyway. For the time being we are filling the black tank by running water from the toilet untill the tank is full, then vacating the tank, which works but is not ideal. I'll tear into it further in a week when we return.
I figure there must be an inline check, or backflow that has failed. I do still have water everywhere else that I need it just no black flush.
2013 Ram Power Wagon 2500 4X4 5.7 Hemi
2001 Airstream '34 Limited
Fulltime in 2013 and LOVING it !!