Although he isn't using the terms exactly the way we would today, Henry appears to be teaching that all baptized infants who die in infancy are saved but that those surviving infancy should not presume they are saved based on their being baptized. I don't think he is necessarily using regenerated in the FV sense wherein there is some kind of temporary union with Christ by way of baptism even for the reprobate. I think the old divines sometimes used the term regeneration to signify the entrance into the visible church. Others who are more well read in this area perhaps could clarify.

Now you answer mine

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Chris Poe
Mandeville, LA

"There are the foolish fanatics always to be found in such a movement and always discrediting it--the lunatic fringe in all reform movements." Theodore Roosevelt