Answer: Rosemary can seem to dry out for several reasons. Over and underwatering can both lead to root damage, with corresponding branches dieing back as a symptom of the root damage. But, since you had your plant for about a year, I would think your watering must have been fine. In general, for rosemary, the soil should drain freely, and a terra cot pot is ideal for helping assure good drainage and air at the roots -- because it allows for evaporation through the sides. (A plastic pot does not.) So I would not expect the different pot to help with that issue.
A buildup of salts from fertilizer use can sometimes cause some root damage. But, the type of pot would not have much affect on that -- your fertilizing practices and lack of leaching would contribute to it. The best way to counter excess salts is to flush the soil periodically, maybe twice a year, with plain water. To do that you would water heavily to the point of runoff several times in quick succession, to flush the salts lower down through the soil and ultimately out of the pot. If your plant was outside in the rain, this would happen naturally. Also, be sure you are not overfertilizing.
I would expect the above types of damage to show up over a large portion of the plant rather than just a branch or two at a time. The limited area of damage suggests a pest problem such as spider mites or mealy bugs or scale, or possibly mildew or fungal infection. I would suggest you examine it very closely to check for evidence of these.
The insect pests can be treated with commercially formulated insecticidal soap per the label directions. Spider mites can also be reduced by providing a lower room temperature -- they increase very quickly in rooms with dry hot air such as we have indoors during the heating season. If one branch is badly infested with spider mites or scale you might trim it off and dispose of it in the trash to try to limit the source.
The fungal problems can usually be controlled through cultural changes. Rinse the plant thoroughly with tepid water to remove powdery mildew, then allow it to dry. Make sure it receives ample light and is in a spot with good air circulation. If it has grown very dense, you could thin it somewhat to allow air and light to better penetrate into the plant.
Finally, a possible cause for dieback after a year might be the need for repotting to a slightly larger pot -- if the plant has grown a lot, that repotting might solve the problem.
I hope this helps you trouble shoot.
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