From my experiences with thrips, they are very difficult to get rid of. I doubt the neem oil will do much (I don't use the stuff anyways). Thrips and mealies are the 2 critters that I only treat with chemicals. What type of insecticide were you using? For thrips you need a systemic, because they tend to hide deep in the plant, where contact insecticides can't kill them. If you do treat with a systemic, make sure to treat 2 or 3 times about 10-15 days apart, to get all the freshly hatched larvae. One that works well is a systemic with imidacloprid as the active ingredient. It's also has the advantage of being relatively "safe" to use in the house, compared to other systemics.
Good luck getting rid of the thrips!