What brand of washes are you using over the Tamiya paint?
How are you cleaning up the excess? Are you rubbing it off with a paper towell or q-tip? You could be simply rubbing through the paint. Try cleaning up the excess enamel wash with a brush that is slightly damp with thinners.This won't work with acrylic washes, you have clean them up before they dry, which is really fast.
Also, try applying the washes on top of the gloss coat, then apply the matt coat when the wash is dry.