Ok so I'm not highly experienced however I have had the same concern as you, I visited pet stores and got 2 possibilities.
1) Could be lots of oxygen in the water therefore the gills don't need to work as much causing loss of gills
2) Poor water quality. The chemicals in your water may be off balance, it can be difficult maintaining good water quality
I suggest taking some water to your pet store and asking for them to test your water and see what the results are. If that comes up all good and there are no other visible symptoms then I would assume there is a high oxygen concentration in the water. If there's a bubbler in the water it might be good to switch that off and see what happens (as long as you have a filter going still)
All on all I would go to the pet shop.
Hope your Axolotls regain their gills soon!