Warning: Math in this post.
AllElseFailed: I have a regular iStick, and the Ohms are displayed on the screen next to the voltage and watts.
The battery in that mini is a 1050mAh battery, which means it can deliver 1050mA for one hour (or 1mA for 1050 hours). The specs on the mini say it maxes out at 10W or 5V, whichever you hit first, so my guess is that it's meant to be used with a 2.5 Ohm coil (that would be a perfect match).
In that configuration, the battery is delivering 2A when you push the button, so it should be able to fire for 30 minutes.
If you have a 1 Ohm coil though, the mini would cap out at just 3.1V to give you the 10W. It would pull about 3A with that 1 Ohm coil, and the batter would only last for 20 minutes of firing.
That battery should be lasting WAY longer than 10 puffs. It should last you all day unless you are breathing through it constantly.