Model: SG5010 Servo Motor
• Type: Coreless Motor With Nylon Gears
• Speed (4.8V no load): 0.17sec/60degree(4.8V)
• Stall Torque (4.8V): ~3.1kg/cm
• Dead Band Width: ~30us
• Voltage: 4.8-6V (Max)
• Dimensions: 40 x 20 x 43mm
• Weight : 38g
Voltage 6V Maximum
I don't know for sure, but I suspect that your 9v battery may not provide enough current to power that servo.
I may also be that the servo is seeing 9v and shutting down to protect itself.
Now that the servo specs are documented, a more knowledgeable member may weigh in.
John