Not wishing to assume what you may or may not already know, but just a friendly comment.
With small taps like 4-40, they are rather weak and very brittle, so easily prone to breakage, and there is no need to ask how I know this. Once you start feeling any real resistance to turning forward, go backwards at least 1/4 turn or until you feel the "chip" break away, before going forward again. The smaller the tap, the more gently I progress, but typically find that a 1/2 turn, or a little more forward, and a 1/4 turn back gets me there without the grief of a broken off tap.