1) APTX can cause the body to revert age and keep it that way and Vermouth toke it
this point can itself be explained in 2 different ways:
1-1) the side-effect of APTX takes x years of whoever toke it (Vermouth was older than Shinishi when she toke the APTX so she reverted to a later age).
This point can be excluded because there's no hint to Vermouth aging which would be needed to the theory (although she could be masked the whole time so I figured out it would be nice to state)
1-2) APTX, when does not kill, only reverts the age of people with less than x years old; only keeping the appearance and body functions of those who were older than x years old (hormonal reasons maybe?)
2) The organization have something more advanced that APTX that grants immortality
This point seems rather unbiased taking in account that the plot runs around Shinishi and the APTX, although it can be a failed attempt of the organization to "revive the dead". (Also it could explain why they were able to keep to good job for 50 years, immortal co-workers sure come in handy.
Since Conan not ever stated something about growing up I guess it can be explained by "1)", or that APTX has a side effect similar to 2) due to it's nature (same resources maybe?)
Well there you go, opinion stated and open to discussion.
Notes: Immortal refers to "not aging" not "can't be killed"
The argument "But, not everyone else around him is growing also!" Won't be heard by my person since it doesn't justify that he's immortal or not, but justifies that I have no reasons to believe that he is, what I in fact don't



