The other thing (or thing and a half) would not really violate the inverse square law, but only seem to violate it. That thing would be an attractive (or repulsive, hence the "and a half" literary vehicle :)) force with a source located so far away as to make the force gradient so gradual as to be below any threshold of measurement. (At close range, the gradient is very steep, at long range, it becomes increasingly consistent.)
So, perhaps there's a large, (perhaps dark) object located somewhere far to the other side of the Sun from the probe, exerting a slight pull, apparently constant due to the great distance from the probe.
However, if the effect is seen on two probes that are aimed in different directions relative to the Sun, then it would shoot that theory down.
Maybe it's just the aether wind, flowing towards the Sun. :)
Or perhaps radio waves don't travel at the speed of light forever. Maybe they slow down by 6 mph every 100 years.
That sort of thing might not be detected until you had a few probes a great distance from this planet.
On another note: isn't it wild that the U.S. has been sending probes into deep space for over thirty years?!
Three decades later most nations on this planet haven't even figured nuclear power out, much less how to send atomic-powered probes into the far reaches of space.
Or, perhaps there is a dispersed gravity source within the solar system that hasn't been noticed yet, not a planet, but a cloud of matter, gas possibly.
Perhaps it is electrostatic in nature, the ship could have picked up a large charge by now.