Phil,
Spray it once (per season) and be patient. It is not a contact spray. The Neem is absorbed through the leaves and ends up in all parts of the plant but it takes a while to get there. Then, any sucky bug that bites the plant will die but good bugs will not be affected.
Although Neem is deadly to sucky bugs, it is safe for humans. In fact, it is used in soap, lotons and shampoos.
PS: Make sure you buy 100% Neem