Dear student,
Microspore Mother Cell(MMC) undergo meiosis only once because meiosis is a reductional division and after each such division, daughter cell (gametes) so formed gets a half number of chromosomes. If this kind of reductional division occurs repeatedly, eventually the ultimate cell would have reduced number of chromosome and would not be able to show the normal characters or finally, a death of a cell would occur.
Meiosis is a vital process for the formation of gametes which MMC does for its formation. Instead of meiosis, mitosis can not occur in MMC because, mitosis is an equational division which is the character of the somatic cell.
Regards.