HIFI is a heterodyne spectrometer aboard the Herschel Space Observatory, providing high-spectral-resolution capabilities. Of its seven frequency bands, four (bands 3, 4, 6, and 7) employ Martin-Puplett diplexers to combine sky signal and local oscillator at the two linear polarizations H and V, prior to feeding them into the mixers (receivers). The optical path difference in each of these 8 diplexers must be tuned to the observed frequency. The required actuator currents were determined in flight before the start of routine science observations. We here report on regular (roughly quarterly) engineering test observations to validate the repeatability of the HIFI diplexers during the routine phase of Herschel operations. We find the optical path difference to be stable to within 0.4 % of the relevant wavelength, typically at the sub-micron level. We conclude that the repeatability and precision of the diplexer tuning mechanism are so high that science data are in no way negatively affected. With the diplexer calibration established and validated, this line of reasoning can be reversed, and the diplexers can be used as relative spectrometers to measure the local-oscillator frequency, i.e., to check the spectral purity of the local oscillator across the diplexer bands. This was done from before launch out to the last months of cryogenic operations in space.