How do I make pom poms not fall apart as easily?
If you want to make the pom-pom not fall apart as easily you have to pull the string tighter when making a knot. Some tips to consider:


loop the string about 3 times before making the final knot
use your finger to hold the string in place when making the knot
try using a different (not yarn) string for the knot – a thin and strong one (so that it doesn’t break when pulled tight)
if you are using the same yarn to tie the knot as the one the pom-pom is made of, and you are using natural yarn, then try soaking the knotting string (just that string) in warm/hot water and make the knot while it is still wet (it should shrink when it dries, giving you a tighter knot)


I guess the reason why pom-pom manufacturers don’t do anything about it being  easy to pull separate strings from a pom-pom is because pom-poms are not meant to have their strings pulled out one by one, and they turn out to be just fine if you don’t do that.

If you feel like you need to use glue anyway, try it, and share your results.