If you are interested in profiling some of the more abundant presented peptides (in your cells of interest) you can be able to get away with a bit fewer cells these days using MS based immunopeptidome profiling. In addition, if it is a targeted effort (not a discovery based profiling) and you know what peptides/sequences you want to profile you can also boost the sensitivity a little bit. However, the number of cells together with the amount of HLA-molecules available (in that specific cell) still dictates the immunopeptidome coverage/sequence depth you can achieve in a discovery experiment.

In the end of the day the MS-instrument is dependent on the conc. of a given peptide (when they are in the instrument for detection competing with all other peptides). It is also sequence dependent, meaning how well a given peptide behave (ionize/fly/fragment) in the mass spectrometer. HLA-II peptides are longer than HLA-I peptides so that helps with increasing the chances of having a couple of charged amino acids present within your peptide.

There are constant improvements of the actual different instruments (in terms of improved sensitivity and scan speed).... but as a very rough guide you can keep in mind that you often need a peptide to be in the very low range of femtomole to be detectable and achieve nice sequence spectra (in a complex mixture). Basically, in some cases there are not that many molecules (peptides) around to detect since some peptides are presented in very low amount (copies) per cell.