We had a similar symptom. The rubber seal between the toilet and the pipe had failed, literally sliced open through years of use. We would clean the whole area and park for storage and the smell would be gone. One flush and the odor returned, robust and nasty.
Waste from the toilet was leaking around the seal and under the tile in the bathroom. A flush would add moisture and reactivate the yuck that was already there.
On our last trip, we removed the toilet and treated the area with an enzymatic odor eliminator. We cleaned the toilet and the area thoroughly. (We also eliminated a bidet attachment from the previous owner.) Then we reinstalled the toilet with a domestic-style neoprene seal from Home Depot.
Problem gone.
Matt B