I use Tamiya acrylics and love them for the reason that they stick very well to the model. I have never peeled any paint off a model when masking (even when using high tack tape!)
however:
I would suggest washing the model first as MKISH suggested. I usually do the whole model first in warm water with mild detergent ...then as I am getting ready to paint sub-assemblies I wash them with Windex. or Tamiya thinner...just dab a Q-tip in either and give a scrub down. Then dry with a lint free paper towel. The surface should be ready.
also:
Are you airbrushing or painting by hand?
if you airbrush, make sure you don't thin the paint to much or overspray....or both. If you overspray or leave a puddle (which often happens when you've over thinned) than the paint doesn't adhere as well (and also takes much MUCH longer to cure) If you do many light coats the colors look much better. Start with an orange peel layer and keep slowly adding until the color is right. This gives you a surface that is strong and can be worked on almost immediatly.
Good luck
James