A fully charged 2000 mA battery should be more than enough for your ignition for a full days flying and then some. Interference from the ignition system can make the rpm jump around all on it's own and so can the carb in a cowled situation. Is the engine cowled and if so have you tried flying it without the cowl to see how it behaves in the air. Considering that all seems to have been working well and just got worst over time there are a few other things you can check or do such as, change the plug, check that the plug cap is on real tight or that the ignition sensor mounting is not loose.

Karol