the gill filaments don't fall out but they can regress, this normally happens if there is something wrong with the water and will re-grow once corrected (although sometimes not as neatly as originally grown).
the gill filaments are fine blood vessels that allow for oxygen to be taken from the water into the blood stream, if there are any toxic substances in the water an axolotl will regress the gill stems and filaments to protect itself, you may find that your axolotl will make trips to the surface more often although it can still absorb oxygen through it's skin.
as for why one axolotl is affected whilst the other isn't is because different axolotls have different tolerances to their environments.
do a full water parameter test ie.. temperature, ph, ammonia, nitrite, nitrate, kh, gh.
ensure adequate/good water oxygenation.
turn sand over weekly to release debris and gasses prior to a water change.
add 2g/l non-iodised salt to the water to help protect and aid recovery.