LBCF 29.2: “Those who do actually profess repentance towards God, faith in, and obedience to, our Lord Jesus Christ, are the only proper subjects of this ordinance.”
The operative phrase is “only proper subjects”. As in the case of “due administration”, this phrase is not self-defining, because “proper” could be taken in two ways.
Either, (a) “proper” refers to that which is “appropriate”, which pertains to congruity of the one with the other thing, the subject and the rite. It could be, therefore, that “proper” non-exclusively qualifies “subjects”, opening the category of “improper subjects”. Such improper subjects are at least subjects.
This does seem a reasonable reading if the statement is considered on its own, however it would have the unfortunate effect of removing from the Confession any express limitation on the subjects of Baptism. Therefore, it is highly doubtful that this was the intention of the original authors.
Alternatively, (b) it could refer to belonging to Baptism, that is, only repentance-professing persons belong to Baptism, meaning it is a nullity if any other is washed in the Triune Name.
Any brief perusal of Particular Baptist writings makes it plain that the latter was intended. The staunchest statements on this matter abound in every tract.
What is intended by the content of the qualification, professing repentance, faith, and obedience to our Lord, is evidently an exposition of the word μαθητής/discipulus, as found in Nehemiah Coxe, An Appendix to a Confession of Faith (1646):
[W]e therefore doe not admit any to the use of the Supper, nor communicate with any in the use of this ordinance, but disciples baptized, lest we should have fellowship with them in their doing contrary to order.
Therefore, the Confession requires baptizands to be disciples, which the Particular Baptists defined as being capable of and actually professing repentance, faith, and obedience—note, it does not require obedience itself, but profession of it.
The question of repeating the ordinance is not actually treated in the Confession. However, given that Baptism is given on profession, it would at least seem unnecessary to rebaptize upon a falling away and subsequent “reprofession”.
Seating Baptism as a sign of present regeneration as Keach does (Gold Refin’d pp82–3), without making this real (which he expressly disowns), does shift much Baptist theory towards a baptized status contingent upon future interruptions, and the natural corollary of true anabaptistry.