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Probably limited a small bit by structural strength, i.e. more acceleration means a stronger and heavier structure. For manned rockets, the G forces are even lower to accomodate the astronauts. So I'm assuming that even lower accelerations are only possible if you trade off fuel efficiency.
There's no such thing as zero G's. Even the two Pioneer spacecraft, launched in the 1970s and now the most distant man-made objects, experience a tug of one 10-millionth of a G from the solar system they've now left. Astronauts in orbit are still subject to about 95 percent of the gravity we feel on Earth.