It was our first trip in the Airstream. We were woken at 4:30AM by the beeping LP alarm. We did not smell propane.
We couldn't figure it out for a while, got on the forums - but nothing seemed to work. Then, we noticed our heat was blowing cool air...
I went out and saw that one of the tanks was closed, so I opened it.
Came back in and the alarm persisted. One of the tanks had gone empty. The heat went back to blowing hot air. Still the alarm persisted...
I opened the vent in the bathroom and left the door open. Soon the alarm stopped and the LED went back to green.
So, try opening a vent!
Best wishes, this never seems to happen during the daytime.