I think it might be an activated immune system OR being in a weakened state. As for why...
Haibara/Shiho: held in captivity and potentially injured when caught rebelling after news of her sister's death. Thus, leading to the immune system running higher than usual.
Mary: This chapter basically confirmed that she was a bit sick when she went to meet the fake Tsutomu, which of course means, the immune system is more active.
Shinichi/Conan: He was assaulted by Gin and sustained a decent injury which of course would have the body run the immune system in order to heal and protect.
In all three cases, the victims health was already comprised so the APTX4869 would either be less or more effective depending on how Gosho wants to write it.
If the "true" effect is dependent on the body fighting off the poisonous effects first, then it's a heightened immune system. However, if it's that the body is already doing too good a job of repelling the drug and only leaving that the poisonous components to kill, then it would mean that the victim needs to be in a "weakened" state so that the body is more susceptible to the "true" effects.
This would also explain why the "cure" works the way it does, as some part of the APTX4869 is potentially sitting strong and active in the now shrunken body, and needs to be weakened/reversed via immune system plus a counter agent.
