As illustrated in the following diagram (A, B, C, D are 4 specified space points, and C is close to a black hole), a small ball at distance of a black hole is stationary (suppose now it's mass is m0) and begins to move towards the black hole along the path ABC due to the gravity of the black hole, so the ball moves faster and faster (now the gravity of the black hole is the unique force exerted on the ball), and its mass increases according to the special relative theory.
A-----------------------------> B ---------------------> C Black Hole
A<----------------------------- D <--------------------- C
After a long time (I think we don't need to care how long the time is), it arrives nearby the black hole at a very high speed, say, 0.99c. But we stop it now in any way (thus its mass reduces to m0; how to stop it? I think we don't need to care this neither -- I just want to release its kinetic energy so that its mass restores to m0; we don't consume our energy for its stopping, on the contrary, we collect kinetic energy from it), and drag it back very slowly along the path CDA (here "very slowly" means we can consider its mass stays at m0).
When the ball was moving on the path ABC, it had a much higher speed and more mass than it was on the path CDA, so, according to the special relative theory again, the black hole did more positive work when the ball was moving along ABC than the negative work done by the black hole when the ball was dragged back along CDA. So, the net work done by the gravity potential field of the black hole is not zero, which contradicts with basic physical laws – the gravity potential field does zero work on an object moving on a closed cycle. What is wrong?
Note: in my question, the black hole could be replaced by a normal star if you like; but using a black hole can enlarge the effect of the special relative theory so that we can image that the mass of the ball experiences great change during its motion.