Anne, what brand paint stripper are you using? Are you following the manufacturer's directions totally? Particularly as regards the time you leave the stripper to work, it is important to follow the directions and having paint left after three courses of stripper is an indication of some other problem--with one exception.
Milk paint is an old product that has been around since the Egyptian pyramid builders. Milk paint has a chemistry that is totally different than modern paints but it was common into the early 20th century. Check out more info at the website of the only current manufacturer of true milk paint--www.milkpaint.com . The best and darned near only stripper that will work consistantly on milk paint is Peel Away 1. You can check this out at www.peelaway.com .