Answer: Based on your description it is difficult to give you a definite diagnosis of the problem, but a common reason is that the branch was physically broken or damaged in some way. If this is the case, simply remove the broken section with a clean cut. Junipers can regrow from old wood, so eventually it should fill in again for the most part.
Another common possibility is that a neighboring plant overhangs that section of the bush. If so, the juniper is simply reacting to lack of light and air. You might consider pruning or moving the neighboring plant.
Another less likely possibility is that spray drift has caused damage. Finally, there are a number of insects and diseases which affect junipers. If you suspect this is the case, you might wish to take a photograph of the entire plant along with a sample of the branch to your County Extension for a positive identification of the problem and suggested control, if any. Their telephone number is 349-1247.
Unfortunately, fertilizing a plant will not solve problems unrelated to nutrient deficiencies. Since this problem only affects part of the bush it is unlikely that it would help in this case. However, you might wish to perform a soil test and see if there any specific amendments or nutrients you might add either routinely or specifically to help the bush recover. The County Extension can help you with the soil test and interpreting the results, too.
I hope your juniper recovers!
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