Powering down during battery switching would be possible if the other solutions are to hard to implement in this particular case but I'm also interested in the general solution on the non interrupted power supply problem using batteries.
I think the following scenario would work:
1) Find a 5V (cell phone type) battery pack that can power the Pi, and has the attribute that you can connect and/or disconnect charging power to the battery pack without this action causing the Pi to crash. These do exist, but they're hard to find and there's no real way to tell from the blurb or sales information whether or not it will work. Most battery packs that you can buy at retail will cause the Pi to crash when you either connect or disconnect charging power. You need to find one that doesn't do this.
2) Hook up a charging circuit to charge the battery pack, with the power coming from a portable 12 v (car battery or wheelchair battery type). This battery can be changed out/recharged/put back as needed.
3) Hook up Pi to run from the battery pack.
Now, the Pi should stay up and running forever. You just have to change out and recharge the backup battery as needed. As long as the Pi doesn't crash from the act of removing the charging power, you should be good to go.