Suppose you are at rest relative to a black hole (so you are maintaining some constant acceleration in order to oppose that gravitational attraction), outside the event horizon. Now a continuous stream of energy starts falling into the black hole. This will cause the event horizon to grow and the gravitational potential of the black hole to increase, meaning that you would begin to fall toward the event horizon (because your acceleration is no longer sufficient to oppose the gravitational potential).
Now suppose that rather than the black hole growing, it remains at a constant size (nothing is falling in), and the observer's acceleration (which is opposing the gravitational force) decreases (his rocket is losing power, but he is unaware and unable to measure this power - I'm thinking along the lines of Einstein's equivalence principle). Again he begins to fall toward the black hole which will seem to him to be increasing in size.
Is there any way for the observer to tell the difference between these two cases (i.e. is there a way for the observer to know that the decrease in distance between him and the black hole is due to an increase of mass in the black hole or a decrease in his own acceleration)?