Single receiver GPS is very good at a two dimensional location, but sucks when you add a third dimension. In order to get a good 3D (lat, lon, elev) location you need to use differential GPS with multiple stations...blah...blah...blah...
In other words the mathematics is letting us down. You'll find that over time your elevation will fluctuate even if you don't move.

... I knew I'd use that geophysics degree for something, someday