A hard drive that spins up and down constantly is usually a sign that it's getting ready to fail. This is because mechanical disk drives spin constantly, and wear and tear on the motor and drive increases during spin-up and spin-down. 

A hard drive that spins up and then spins down after a few seconds may indicate a problem with one or more of the read/write heads. Other reasons a hard drive may spin down after turning on include:
Weak power supply: The hard drive will try to spin up, but may not be able to reach the required RPM, causing it to spin down and try again.
Outdated or corrupted drivers: The computer may not be able to detect the spinning hard drive.
Computer is set to turn off devices automatically: This may turn off the connected external hard drive sometimes. 

A hard drive can spin down for a number of reasons, including:
Power supply
A weak power supply may prevent a hard drive from spinning up, or cause it to spin down and error.
PCB
A damaged PCB can prevent the drive from receiving power, causing the motor to not turn. The PCB can fail due to incorrect component placements, overheating, or power failure.
Environmental factors
Exposure to fire, water, high magnetic fields, sharp impacts, or environmental contamination can lead to a hard disk failure.