I think the mass actually changed. If you move, your mass increases w.r.t to an inertial frame. The closer you travel to the speed of light the more mass you get. I think mass also changes when the gravitational field changes. The device picked up those small changes .
It was not changing, the data was being corrupted. The link you gave describes relativistic (not invarient mass) in special relativity. You are correct that the relativistic (NOT invariant) mass can change depending on the inertial reference frame. However, the inclusion of changing gravitational fields and acceleration within gravitational fields is not the special theory of relativity, but the general theory of relativity.
While your idea of varying inertial reference frames is correct for invariant mass at a constant velocity (or experiencing no acceleration or distortion of spacetime due to a gravitational field), it is not correct when those are included.
In fact, it is easy to see that the relativistic mass must stay constant here for two reasons: 1) Relativistic mass can change between reference frames, but we are always doing the experiment in the same reference frame, and 2) Look at the equations. http://en.wikipedia.org/wiki/Lorentz_transformation#Lorentz_...
There are no gravitational terms in those equations, only spacetime derivatives (and various constants).
Edit: It's very late and I bet I'.m being unclear -- the velocity magnitude is probably changing slightly because of the outside fields. However, I doubt that relativistc mass change would be detectable by even their instruments. It's probably just variance in path.
"So the bigger lake in the Spring was making the particle heavier."
I am not sure which effect the quote describes: a slight change in the mass or a change in the instrument. Both are different. If it is the former I should be able to measure the change from light years away (since the lake wont affect me but will affect the particle).
http://en.wikipedia.org/wiki/Mass_in_special_relativity