Black Spots on Bay Tree

We live in Western North Carolina, USA, in a hardwood forest with beech/oak/hemlock/black walnut trees and mountain laurel. Last fall I bought a 3 ft(1 m) bay tree from a local nursery. I kept it inside in a cool south facing room with large windows through the winter and spring. It grew new leaves at the branch tip in the spring. Late spring, we repotted the tree when we put it outside on the deck. After a period of good growth, around mid-summer, it began to have small black spots on the underside of the older leaves. After a while they turned yellow and fell off. I took some of the leaves to the nursery and they suggest neem oil. I used it a couple of times, but each use seemed to accelerate the yellowing. Now, all of the leaves have spots and we have lost about half of leaves. Any help would be greatly appreciated.

Bay laurel is rated for zone 8 to 10. Since you live in zone 7, summer heat should not be a problem. However, since the plants spend the winter indoors, the leaves might have problems with the exposure of a deck, so I would try placing them in half shade when out of doors. A clue would be if the black spots do not develop on new leaves when the plants are placed indoors for the winter. Also neem oil (always used with dish detergent as an emulsifying agent) must not be used in full sun, because the oil may temporarily block stomates and thus stop the plant from cooling itself by transpiration. The emulsifying agent may also wash off the protective wax coating of the leaves and the leaves then dry out and die. Over-fertilization can also cause black spots on leaves, with blackening being usually heaviest at the edges.
Another cause could be a fungal or bacterial infection. The nearby forest could be the source of spores. Try spraying with such natural fungicides/bactericides as "flower" of sulphur in water, 3 to 5% hydrogen peroxide and in bad cases rubbing alcohol. You can also try a drop or two of tea tree oil per litre of soapy water as a spray.