The tennis ball falls off the shelf and bounces several times. Each bounce is lower than the one before. Soon the ball stops. Why doesn't the bar keep bouncing?

The tennis ball stops bouncing due to energy dissipation in the compression and decompression process.

Explanation:

When the tennis ball collides with the ground, some of its energy is dissipated in the compression and decompression process. This process keeps on repeating and then a time comes when all of the elastic energy in the ball is exhausted and the ball stops bouncing. At this point, the elastic energy stored  in the ball is so small that it cannot overcome its own weight therefore, it stops bouncing.

this is poiselle's equation from fluid mechanic in physics. mech eng

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft