Do you have more room? Can you fit something slightly larger in, maybe something longer? A 6 cell AA pack will last a lot longer than a 9V radio battery.
9V alkalines don't pack much punch, note that the best on this list is 490mAh at 100mA draw but that is for a brand I've never heard of. The other alkalines are more in the range of 300mAh, with capacity going down a lot at 500mA current:
Whereas a 1.5V AA alkaline is over 2Ah at 100mA, and still over 1Ah at 500mA:
6 cell AA holders:
Enclosed with a power switch:
Powerjack for Arduino already installed:
Or use an Ultralife Lithium 9V battery.