I have experienced this problem, too, and noticed that the names of the textures are included, but the textures themselves are not imported.
In some cases, I have gone through each of the textures in the list and manually created the nodes for them, using the image texture files that were supplied with the model. It can be tedious if there are a lot of textures, but it works.
Once I have recreated all the textures, I usually save the model in a Blend file in my model library and delete the obj version. When I save the model, I pack the textures into the blend file so that they don't get lost.
(To do this, check the box in File -> External Data -> Automatically pack into .blend)