You need to do an experiment. YOu'll need an accurate thermometer. Right after the burner finishes heating things up, take a small sample of water to determine the starting temp. Turn the burner off so it can't run. Either overnight, or preferably more often, take another small sample to develop a curve of how fast the temp drops (the quality of the insulation). Knowing how many hours it takes to cool off the tank's worth of water, you can figure out how many BTU's it would take to just keep it hot. If you are really lucky, the specs are available on the manufacturer's website, but they often have the tank at a nominal 70-degrees. The bigger the delta between the room temp and the water temp, the faster the thing loses heat.
You also might get an idea by monitoring how often the burner turns on when there is no useage. This would require knowing and believing the accuracy of the thermostat and its repeatability. Say it allows a 10-degree drop before it turns back on, and it takes 4-hours, with 40-gallons, you can figure out how many BTU's it is losing. 40 gallons * ~8 pounds, * 10-degrees = BTU. Extropolate that for the time it would take to get to the room temp.