If you are looking in the IGI they always put pre-marriage or illegitimate children under the mother's name, although this does not usually reflect how the entry appears in the register. The register usually reads something like "John illegitimate son of Mary Smith and Tom Brown...", or just John illeg son of Mary Smith. The Isle of Man custom was to call the child by his/her father's surname, whether or not he was named at the bapt. So this first child you mention won't have vanished. If the mother later married the father (very common) the child would be under his surname in censuses or wills etc. If he/she had a different surname he/she is often found with a grandparent in censuses, or sometimes with the natural father's family. (Or buried under the father's surname.)

Sue