I'm not able to keep the battery charged directly with the Arduino because it's a Lithium-ion battery. It has to be recharged once a week. I'm thinking about cutting off the battery entirely and just powering it with the 3.3 v pin on the Arduino. I'll update later.
I'd suggest that would be the best thing to do - I'd have thought it would be fine with 3.3V personally - make sure it doesn't require more than 50mA (if it's going to be powered off a duemilanove/old mega - 200mA I think if it's an uno/new mega - I'd go check that to be sure though)