Star of Bethlehem is a bulbous plant that, as you have discovered, is difficult to get rid of once established. Roundup will usually burn them back, but because they have a lot of stored energy in their bulbs, they can resprout. Digging can be effective in removing them, but you have to dig deeply, and may have to sift the soil to avoid missing small bulblets. Persistence at mowing off or chopping off newly sprouting plants can also work, but you'll need to keep at it weekly for a full year. Sorry that there isn't an easier way.