Let d be the distance (in some coordinate system) from a particle to the event horizon of a black hole. For a particle starting at distance d>0 above the event horizon to rise away to a very large (infinite distance) would require an energy E. As the initial distance d shrinks to zero, E rises without limit (to ∞). At d=0, the particle is at the event horizon. Alright, reverse this sequence.....the particle falls back toward the event horizon from a large distance. It would seem that the limit of kinetic energy E acquired by the particle would be infinite as d shrunk to zero. Since this is clearly not possible, the particle should not be able to cross the event horizon (in either direction). The issue remains even if the acquired kinetic energy is radiated away or converted to mass, since the potential well is still infinitely large.
Where is the flaw in this scenario?