  We study the 205.9 Hz pulsations of the accreting millisecond X-ray pulsar
NGC 6440 X-2 across all outbursts observed with the Rossi X-ray Timing Explorer
over a period of 800 days. We find the pulsations are highly sinusoidal with a
fundamental amplitude of 5%-15% rms and a second harmonic that is only
occasionally detected with amplitudes of <2% rms. By connecting the orbital
phase across multiple outbursts, we obtain an accurate orbital ephemeris for
this source and constrain its 57 min orbital period to sub-ms precision. We do
not detect an orbital period derivative to an upper limit of $ | \dot{P} | \leq
8 \times 10^{-11}$ s/s. We investigate the possibility of coherently connecting
the pulse phase across all observed outbursts, but find that due to the poorly
constrained systematic uncertainties introduced by a flux-dependent bias in the
pulse phase, multiple statistically acceptable phase-connected timing solutions
exist.
