Polar molecules in selected quantum states can be guided, decelerated, and trapped using electric fields created by microstructured electrodes on a chip. Here we explore how nonadiabatic transitions between levels in which the molecules are trapped and levels in which the molecules are not trapped can be suppressed. We use (12)CO and (13)CO (a (3)Pi(1),v = 0) molecules, prepared in the upper A-doublet component of the J = 1 rotational level, and study the trap loss as a function of an offset magnetic field. The experimentally observed suppression (enhancement) of the nonadiabatic transitions for (12)CO ((13)CO) with increasing magnetic field is quantitatively explained.