A number of us were having problems duplicating the textured dynamite stick. I have found the solution to the problem.
The issue is the way that the "texture supports" are being copied. Texture supports are the "frame" that holds the texture - the texture is not wrapped directly onto the model but onto the support. This give more flexibility but also adds another complication to watch out for! They appear as green wireframes.
There are different options on how the supports are copied when an object is duplicated. These option are accessed through Edit > Duplicate/Instantiate Options (see below):

The "Texture supports" options must be set to either "Always duplicate" or "Freeze projections". Here is a summary of the four possible options:
Only if selected The support is duplicated only if it is explicity selected. The duplicated model then shares the same texture support as the original object. This means that the copied object will be squeezed onto the same texture in the texture image. (This is the problem most of us were having.)
Alwasy duplicate The support is duplicated whether it is copied or not. The support appears in the same position in the duplicates hierarchy.
Alwasy share Never duplicates the object's texture support (similar to "only if selected").
Freeze projections duplicates the object but freezes the texture projection of the duplicate. The duplicate has no texture support. Unless you want to manipulate the texture support of the duplicated object, this appears to be the simplest choice.
