It seems that labeling is not possible in the actual versions of QFIELD any longer (I'am working with 0.8.2 now) when there is a scale-based expression There is no labeling in this case although the new "busy-indicator" shows after disappearing - that rendering /labeling came to an end.
Working for example with a simple
ASE WHEN $scale <2000 THEN "fieldname" expression does work in QGIS 2.14/2.16.2 but not in QFIELD (its the same with using variables instead of numbers for the scale). Simple labeling without expression works without problems.
(I am using a sqlite-database with a multipolygon-geometry for the test with Android 5.0.1.) (In my regular project I use more complicated conditions to build different contents by a scale-based expression - this very simple example might have worked by other settings in the labeling-gui - but I tried to find out where the problem lies)