There are indeed a few options. I paint bodies for a big Halloween dance party. I work in my studio with client traveling up to an hour to get to me...then back home or onto the party....so there are always durability concerns.
Mehron Powder mixed with Mehron Mixing Liquid (thread here noted final set) will stay put...but it does tend to crack in body folds after long wear, will rub off somewhat if your hugging folks and it not the top choice for overall comfortable wearing...it tends to dry and feel stiff on the skin.
If I am painting them with cake paint I use Kryolan Fixing Spray under and over Wolfe Hydrocolor body paint. Most often I use Endura alcohol airbrush makeup. Hands down airbrush is your best best. Both keep a shine.
A new option for linework is DIPS a hybrid body paint....very durable but not good for overall base.