i) To my knowledge, Baptists think the administration of baptism should be contingent on faith. On a credible profession of faith.
That may be age-appropriate. They don't necessarily demand the same thing from a 10-year-old as a 20-year-old. I also suspect Reformed Baptist churches have a higher standard for what constitutes a credible profession of faith than easy-believist churches.
But the basic principle is that children before the age of reason shouldn't be baptized. And after a child reaches or passes the age of reason, baptism is conditional on his desire to be baptized, along with a credible profession of faith.
ii) With that in mind, there's a striking parallel between infancy and dotage. In old age, or sometimes sooner, some adults become feeble-minded. Their short-term memory goes, then their long-term memories goes. They lose their reasoning ability. They eventually lose consciousness.
It's as if they are regressing from adulthood to childhood to infancy. Reversing the stages of cognitive development. Indeed, it's called "second childhood."
Some Christians who become senile were baptized as older children, teenagers, or adults. Their baptism was contingent on a credible profession of faith.
But there's now a sense in which they lost their faith. Not because they renounced the faith, but because they lost the intellectual ability to have faith. In a sense, they will die unbelievers–but not apostates. Much like if they died in infancy.
Then you have Christians who were baptized as babies, in the hope and prayer that by growing up in the faith, they'd grow into the faith. Sometimes that happens, and sometimes not. But in their case they became what their baptism represented. They became believers.
But now that they are senile, they have reverted to the same cognitive condition they were in when they were baptized as infants. They've come full circle.
Whether a senile Christian was baptized before he came to faith, or came to faith after he was baptized, at this point he is like a child before the age of reason. Or even like a baby who sleeps most of the time.
Yet if senile Christians were ever in the covenant, they remain so, despite their dementia. And their membership in the covenant community doesn't lapse when they lose their mind and memory.
That's a special case, but hardly a rarity. Indeed, one of the cruel ironies of modern medical science is that we probably have a higher percentage of senile men and women than ever before. Due to medication and surgery, many people who would have died at a younger age live much longer. And the longer they live, the greater the risk of becoming senile.
Many baptized believers will enter a second childhood which parallels their condition when they were baptized as infants. A spiritual symmetry. They return to God as they came from God.