an extra cell added in series will give you more voltage, but not more runtime.

With small servos in on-road cars we get about 11 mah per minute draw from a receiver pack, I'd expect that to be higher with your servo - maybe 15 mah or more. At this rate, you'd lose 1800 mah in 120 minutes (2 hrs) which sounds about right to drain a 2000 mah pack