Why do objects not fall faster if you wait?
I think You are confused about why the ball falls in the first place. The ball does NOT fall "because the space ship is in motion". The ball falls down because it is an acceleration motion as opposed to motion (in a straight line) with uniform velocity.
Consider a spaceship moving "upwards" (in the direction of the roof of your room-like ship) with a constant velocity v relative to the earth . Everything in your ship has the same velocity v so there is no relative motion. Now, when you release that ball from your hand (without giving it an impulse) there is no change in the velocity of the ball and thus the relative velocity between the floor and the ball remains 0. The ball simply floats.
Now, consider a spaceship accelerating at 9.81 ms^-2 upwards due a thrust force acting on it. You hold a ball stationary above a height. Lets see why everything appears stationary from an inertial frame. The ship accelerates at g due to thrust. You accelerate at g due to the normal force exerted on you by the ship. The ball accelerates at g due to frictional force from your hands. Everything has the same acceleration (and velocity) and there is no relative motion.
Now, at some time T, when everything has a velocity V relative to the earth, you release the ball, which causes the friction accelerating it to disappear. As a result, the ball maintains its velocity v whereas everything else continues to experience an increase in velocity ΔV=a Δt relative to the earth and to the ball, causing it to "fall" to the ground.
Coming back to your question, whether or not the ball falls depends on if the ship is accelerating, and the time taken for the ball to fall depends on increase in velocity of the floor relative to the earth, NOT its instantaneous velocity at the point of release
No matter how much time you let pass, the increase in velocity over the course of the fall always remains the same (assuming acceleration doesnt change)