With your array if your offset is correct then each of the array duplicates will be exactly adjacent to the next which means that you will have overlapping vertices.  When you apply the array modifier then remove doubles you are "welding" those overlapping vertices together.  With your mesh, the duplicates are not overlapping with a small enough threshold so removing doubles will not actually achieve anything.

There is nothing wrong with modelling the stitching just keep the level of detail at the lowest level whilst still achieving the look that you want. 

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