Maybe all the times Dumbledore took Felix Draco was in the Room of Requirement. It would have been bad to catch Draco red-handed because Dumbledore would have had to do something about it, forcing Severus to kill him too soon. It's a bit lame - surely if Dumbledore was looking for lucky opportunities for his searches he would have tried different times of day, and he shouldn't have been too concerned for long term effects when he knew he would be dead one way or the other by summer.
Anyway, I'm sticking to my version that Severus took Felix when he knew Voldemort was on the way to Hogwarts and this allowed him to go prepared for his encounter with Nagini, so he could fake his death and escape to anonymity.
Anyway, I'm sticking to my version that Severus took Felix when he knew Voldemort was on the way to Hogwarts and this allowed him to go prepared for his encounter with Nagini, so he could fake his death and escape to anonymity.