Using observations with e-MERLIN and the VLA, together with archival data from ALMA, we obtain high-resolution radio images of two binary YSOs: L1551 IRS 5 and L1551 NE, covering a wide range of frequencies from 5-336GHz, and resolving emission from the radio jet on scales of only ~15au. By comparing these observations to those from a previous epoch, it is shown that there is a high degree of variability in the free-free emission from the jets of these sources. In particular, the northern component of L1551 IRS 5 shows a remarkable decline in flux density of a factor of ~5, suggesting that the free-free emission of this source has almost disappeared. By fitting the spectra of the sources, the ionised mass-loss rates of the jets are derived and it is shown that there is significant variability of up to a factor of ~6 on timescales of ~20 years. Using radiative transfer modelling, we also obtained a model image for the jet of the southern component of L1551 IRS 5 to help study the inner region of the ionised high-density jet. The findings favour the X-wind model launched from a very small innermost region.