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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.
The gravitational acceleration that the Moon experience due to the gravitational attraction from the Earth is given by: a g =G(M Earth +M Moon)/r 2. Where G is the gravitational constant, M stands for mass, and r is the radius of the orbit. The centripetal acceleration is given by: a centr =(4 pi 2 r)/T 2. Where T is the period.