I mean, if you leave them outside, it's like leaving a block of ham on the floor with a dog in the house: eventually the inevitable will happen.
Neem is usually called a "maintenance" sort of spray because if you really wanted to kill all the bugs you'd use pyrethrins and all that bayer 3 in 1 spray to nuke everything to orbit and make anything else that lands croak too for a couple months. Neem will wreck the current generation of bugs, but considering its short shelf life when you mix a new batch from oil, it's not going to stick around for too long so you'll get a re-infestation from new bugs that land that didn't get hit (which wouldnt' happen in a greenhouse/your house/etc.).
Of course, it doesn't smell as vile as the other pesticides to me (I think they all stink like formaldehyde) is why I just spray neem once a week. Lets me have a good excuse to spend some quality time with my plants once a week too .