The limit is the escape velocity of the orbit.

Not really. The thing is, you're not so much stockpiling kinetic energy as you are using the mass of the body to amplify the force you apply. There is an optimal time to apply that force, which is when you are closest to the body you are orbiting.

So what may happen is if you have a low-thrust engine, you will do a burn at the optimal time, then stop and wait an orbit until you reach the optimal time again. But you're not "stockpiling" anything so much as you are just thrusting at the optimal time. And once you reach escape velocity you have to keep thrusting, there is no more opportunity to do another pass.

I can't recall which probe, but NASA has used the same body for multiply slingshots. But that's stealing orbital energy from the body you pass in the same direction it's orbiting.

I think the mass of the body only matters in how much momentum it has. If you fly by an asteroid you will deflect its course. You could convert the entire mass of earth into spaceships and slingshot them past Jupiter and it would barely register.

You could make multiple passes, if needed, gaining a + delta V each time by designing the orbit such that the spacecraft is on a transfer orbit back to PBH to make another pass. (If, as guelo mentioned, you did not at some point reach escape velocity of the solar system at that orbit.) It would be a very long wait between passes though...

Seems like a Jupiter gravity assist would always be much more practical.