My servo is clicking.

I currently have a project I'm working on that uses a servo to rotate a metal bar. When I run power through my servo, there is a clicking sound that happens. When I rotate it, and it reaches the new position the clicking becomes continuous. Any idea what is causing this and if it is the sound of my servo being damaged. I am using a HiTec HS-625MG.

The clicking is probably the power supply dropping because of a too steep increase of current or a too large current in general.
After searching a bit, some site stated that these servos take 500 mA while moving without load, and supplied with 6 Volts.

What power source are you using ?
Does it have enough spare juice to power that servo (with load) ?

I am using two 3 volt batteries that end up with a total voltage of 5.8. The load I am using is 30g.

You need 1A or more for a small servo.

Measure the voltage with a multimeter.
Do you see the voltage dropping while the servo rotates ?

I measured the voltage while the servo rotated and it dropped between 1 and 3 volts.

That means the current is too high for your batteries.
Keep MarkT's rule of thumb, and use a supply that can handle 1 A per servo.
That will not drop to half the rated voltage.