  Recent work suggests that the mass-loss rate of the primary star (Eta A) in
the massive colliding wind binary Eta Carinae dropped by a factor of 2-3
between 1999 and 2010. We present results from large- (r=1545au) and small-
(r=155au) domain, 3D smoothed particle hydrodynamic (SPH) simulations of Eta
Car's colliding winds for 3 Eta A mass-loss rates (2.4, 4.8, and 8.5 x 10^-4
M_sun/yr), investigating the effects on the dynamics of the binary wind-wind
collision (WWC). These simulations include orbital motion, optically thin
radiative cooling, and radiative forces. We find that Eta A's mass-loss rate
greatly affects the time-dependent hydrodynamics at all spatial scales
investigated. The simulations also show that the post-shock wind of the
companion star (Eta B) switches from the adiabatic to the radiative-cooling
regime during periastron passage. The SPH simulations together with 1D
radiative transfer models of Eta A's spectra reveal that a factor of 2 or more
drop in Eta A's mass-loss rate should lead to substantial changes in numerous
multiwavelength observables. Recent observations are not fully consistent with
the model predictions, indicating that any drop in Eta A's mass-loss rate was
likely by a factor < 2 and occurred after 2004. We speculate that most of the
recent observed changes in Eta Car are due to a small increase in the WWC
opening angle that produces significant effects because our line-of-sight to
the system lies close to the dense walls of the WWC zone. A modest decrease in
Eta A's mass-loss rate may be responsible, but changes in the wind/stellar
parameters of Eta B cannot yet be fully ruled out. We suggest observations
during Eta Car's next periastron in 2014 to further test for decreases in Eta
A's mass-loss rate. If Eta A's mass-loss rate is declining and continues to do
so, the 2014 X-ray minimum should be even shorter than that of 2009.
