you can stop losing levels if you spend a little and train your pets to level 20+.
http://www.neopets.com/~triduo <--- a lab map price guide. it's frequently updated. one set costs around 1mil nps now.
Not true. I have a pet that's lvl 200+ and I still frequently lose levels with the lab. what can't happen is the lab can't send your pet back down to lvl 1.