If you keep feeding a black hole, it will keep growing. But they’re very slow messy eaters. If you have a lot of material falling into the black hole, that material will collect into what’s called an accretion disc. In that disc, the friction from all of the matter spinning about makes it glow so much that the heat radiation pushes it away from the black hole, denying it most of the meal until what’s closer in gets gobbled up. But even that doesn’t get fully eaten. Through processes that are still not fully understood, a good part of that matter is pushed perpendicular to the axis of rotation and becomes powerful relativistic jets that shoot out at a good portion of the speed of light.
So, the answer is that, while there’s no upper limit on how much can absorb, there *is* a limit on how much it can absorb at any one time. And, the more you try to feed it at once, the bigger the mess it produces during its meal.
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