Depends on the battery and the current. If you look at the 100ma curve posted in this link yours will last longer with the low discharge current. So picking one in the middle the time would be greater than 350ma hours / 6.5 ma or around 53 hours.
I think you skipped a decimal, it would be more like 100 hours. I thought 9V batteries were 500 mA/hr ballpark? That would be around 80 hour ballpark at 6.5 mA.